Here is a solo variant I have come up with. It's only partially tested so far and seemed to work well, though having a few more people test it and feedback would be excellent. Let me know how you go with it. Enjoy!
Choose 5 characters to control. All skill cards are kept face up in front of the character's card.
Deal the loyalty cards for a 5-player game face down to each character. You may not look at these cards except by the use of special game text (such as Baltar's ability).
Seed the Destiny Deck with three of each type of skill card instead of two. Always replenish with three of each type whenever it is exhausted.
Characters take their turns in turn order, as usual. The character currently taking their turn is referred to as the "active character". Only the active character may contribute cards to skill checks in the normal way (see "Skill Checks" below). However, any character may play a card for its special ability as in the normal game. You may also use character abilities of non-active characters at any time (providing they are not "action" abilities, of course).
HIDDEN / REVEALING CYLONS
At the start of each character's turn reveal the top two cards from the Destiny Deck and choose one (if the colour of either card matches the colour of the active character, then that card must be chosen. If both cards match the colour, then you must choose the highest-valued card). The current character randomly reveals one of their unrevealed Loyalty cards if the value of the chosen card with the following modifiers equals 7 or more (then discard both cards):
+1 per distance travelled,
+2 if the colour of the card matches the colour of the character (i.e, green leadership card for a green military leader),
-4 per previously revealed Cylon
If the revealed Loyalty card is You Are Not A Cylon, then nothing happens. Leave the card face up for the rest of the game.
If the revealed Loyalty card is a You Are A Cylon card, the Cylon is revealed as usual and their reveal effect is carried out. A Cylon that is revealed keeps his three highest-valued cards, with priority going to cards from decks closest to the back of Galactica (i.e, Engineering first to Political last).
When making skill checks, only the active character may add cards to the skill check in the normal way. Cards added from other characters (including revealed Cylons) are instead first *discarded*, then a number of random cards from the matching skill deck are added to the skill check; for each 1-3 strength card you discarded add 1 card to the skill check, and for each 4-5 strength card you discarded add 2 random cards.
Additonally, rules for the Destiny Deck change while there are hidden Cylons. These rules only apply before the Sleeper Agent phase while there are no revealed Cylons, and only after the Sleeper Agent phase while there is at least 1 hidden Cylon: for skill checks that only require *two* different types of skills add 1 extra card from the Destiny Deck into the skill check. For checks that require four different types of skills add 1 less card (this represents the hidden Cylon players interfering with the human's plans).
Revealed Cylons will always add 1 negative card to skill checks if possible, which will always be their highest valued card of the type closest to the back of Galactica (remember, this card will be always be added using the discard/draw random method described above for non-active characters).
CYLON PLAYER'S TURN
When drawing skill cards for the Cylon player, always draw from either the Engineering or Piloting decks first. To determine which deck to draw from, look at the Cylon player's hand and draw from the deck in which the Cylon player's highest-valued card is lower in strength (for example, if his highest valued Engineering card was 4 and highest valued Piloting card was 2, he would draw a Piloting card). If there is a tie, then the Cylon player draws from the deck in which he holds the least number of cards. If still tied he draws a Politics card.
At the start of each revealed Cylon player's turn, reveal and discard the top card from the destiny deck. The Cylon player's action is determined by the strength of the skill card drawn and if the Cylon player has a Super Crisis card available or not (if the action chosen by the Cylon player is not valid, i.e - Cylon Fleet when there are no Cylon ships on the board, then the Cylon player chooses the next Cylon location to the right, with the Resurrection ship "wrapping around" back to Caprica if the Res. Ship is not a valid choice):
Cylon player has a Super Crisis card:
1 - Caprica (normal crisis)
2 - Caprica (super crisis)
3 - Cylon Fleet
4/5 - Human Fleet
Cylon player does not have a Super Crisis card:
1 - Caprica (normal crisis)
2 - Cylon Fleet
3 - Human Fleet
4/5 - Resurrection Ship
The rules for each location change as follows:
Caprica (normal crisis) - flip the top card of the crisis deck and resolve it normally. Then flip the top card again - if it has a jump prep icon, place it at the bottom of the deck. Otherwise, replace it at the top of the deck. If ever a crisis card gives the current player a choice, roll a die - 1-4: the Cylon player chooses the first option, 5-8: the Cylon player chooses the second option.
Cylon Fleet - flip and discard the top two cards of the crisis deck. Resolve the Cylon fleet activation icons on both cards. If both cards show the same icon, resolve only one of those icons.
Human Fleet - the Cylon player will steal from the hand of the character with most cards in their hand (ties go to the character next in turn order). The Cylon player will steal the highest strength card the character holds, ties going in skill deck order from the back of Galactica.
Resurrection Ship - the Cylon player gives an unrevealed Loyalty card he may still hold to a random character (if there is still a hidden Cylon) following the rules below for selecting random characters. He then draws a new Super Crisis card (which is kept face down until revealed).
When jumping the fleet, if any of the Admiral's Loyalty cards are still unrevealed do not draw two cards from the destination deck. Instead, simply flip the top card and resolve it normally.
If all of the Admiral's Loyalty cards are currently revealed as You Are Not A Cylon cards, then you may draw two cards from the destination deck and choose between them, as normal.
If ever the Admiral is revealed as a Cylon, immediately remove the highest-valued distance travelled card from the card row - the fleet hasn't travelled as far as you thought!
When drawing Quorum cards (including the President's starting Quorum card), do not look at them. Instead, place them in a face-down "Quorum stack" near the President's character card. Whenever the President wishes to play a Quorum card, draw a number of cards from the top of this stack dependant on the following conditions:
If the President currently holds any unrevealed Loyalty cards, draw two cards. You may choose to play one of these cards.
If all of the President's Loyalty cards are currently revealed as You Are Not A Cylon cards, draw three cards. You may choose to play one of these cards.
Any cards drawn that you choose not to play may be placed either at the top or bottom of the Quorum stack.
If the President is ever revealed as a Cylon, immediately discard all but the bottom three cards from the Quorum stack.
Whenever a card instructs any non-active character (i.e, non-active human characters or revealed Cylon players) to "choose a character", then this choice is made randomly. Roll the die and count that many characters forward in turn order to determine the target.
Cards that allow you to look at another character's loyalty cards do not "reveal" that card for the purposes of these rules. However, they may give you a clue as to whose once-per-game ability you should use sooner rather than later, and who you should keep the Admiral and President titles away from!
CARD CHANGES AND CLARIFICATIONS
You Are A Cylon - May Damage Galactica: Draw the five damage tokens. The Cylon player will choose tokens in the following order (ties broken randomly):
1) Location with the most crew members present.
2) Resource token (fewest remaining first).
3) Empty locations.
Investigative Committe: Allows to to play cards into skill checks directly from non-active characters' hands (without using the discard/draw random method described under "Skill Checks").
Assign Mission Specialist: As with the Admiral above, if the character chosen to receive AMS has any unrevealed Loyalty cards, draw only two destination cards instead of three. If the character's Loyalty cards are all revealed as You Are Not A Cylon cards, then draw all three destination cards. If the character is revealed to be a Cylon while AMS is in play, remove the highest-valued destination card from the card row.
OPTIONAL (UNTESTED) RULE
Instead of allowing any character to play a card for its special ability, use these rules instead:
* Any card held by the active character may be played by *any* character, without restriction. For example, if the active character holds at least one Evasive Maneuvers card, then you may choose to play an Evasive Maneuvers card from any character's hand without restriction.
* If you wish to play a card from a non-active chracter's hand of which the active character does *not* hold a copy, then that character must hold at least one additional copy of that card for each unrevealed loyalty card he holds (though still only one copy is played). For example, if Baltar is a non-active character with two unrevealed loyalty cards, and you wish to play Investigative Commitee from his hand (and the active character does not hold a copy of Investigative Committe), he must hold at least three copies of Investigative Committe to play one of them.