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.
These are my results:
1. Pope Benedict XVI and Professor Bunsen Honeydew (Muppets)
Yes, that could work ... "Here, Benedict, hold this wire..." -- "meep"
2. Carter (Nightingales) and Dilbert (Dilbert)
Oh dear. That could be very strange indeed.
3. Doctor Who and dougs
I'm actually very pleased about this. I think I'd learn a lot.
4. a Haggis and ursinehenry
I'll leave it to someone else to write this one. It could be entertaining.
5. Prostetnic Vogon Jeltz (Hitchhiker's Guide to the Galaxy) and Jesus (Bible)
"Blessed are the meek ... oh wait, that doesn't work..."
6. John the Baptist (Bible) and Joseph (Bible)
"You're a loony." -- "You think I'm bad? Have you seen what your son's been doing?"
7 Mary (Bible) and Missy as a SWB (photomanipulation)
Pray for us now.
8. Monique (Sinfest) and Mulcahy (M*A*S*H)
"You know, I'm not sure you're cut out to be a nun."
9. The Pointy-Haired Boss (Dilbert) and Percy (Sinfest)
So long as PHB doesn't confuse Percy with Catbert ...
10. Pooch (Sinfest) and Radar (M*A*S*H)
This one, I think, might really work. Radar's very fond of animals.
11. scarlatti and the Shepherds (Bible)
I'm sure their rod and staff would comfort her.
12. Slick (Sinfest) and the Wise Men (Bible)
"However, they were warned in a dream not to visit Slick on their way back, so they returned home by a different route."