Make a list of all the characters in your icons. (Although you may have more than one icon of a single character, they only go on the list once.) Alphabetize it. Take the first two people on the list; that's your first pairing. Second two people; second pairing. etc.
Kupono Aweau (So You Think You Can Dance)
Eric Balfour (real person)
Jayne Cobb (Firefly)
Billy Desmond (Conviction)
Remy "Thirteen" Hadley (House)
Christina Finn (Conviction)
Claire Fisher (Six Feet Under)
Kathryn Janeway (Voyager)
Jack McCoy (Law & Order)
Morgan (The Texas Chainsaw Massacre)
Brian Peluso (Conviction)
Megan Reeves (Numb3rs)
Kayla Randomski (So You Think You Can Dance)
Adam Schiff (Law & Order)
Eliot Spencer (Leverage)
Pairings:
Kupono Aweau/Eric Balfour - Haha! I think I like the idea of this one:)
Jayne Cobb/Billy Desmond - Um...I don't really know how this would work, but Billy might get hurt
Remy "Thirteen" Hadley/Christina Finn Interesting. Maybe in college
Claire Fisher/Kathryn Janeway - I could see them getting along
Jack McCoy/Morgan - Now I'm picturing a young McCoy getting high in the back of a van in Texas. Odd.
Brian Peluso/Megan Reeves - He would hit on her and she would be amused, but uninterested
Kayla Randomski/Adam Schiff He's old enough to be her grandfather.
Adam Schiff/Eliot Spencer - Eliot would give Adam a headache.