So, I found one online. Mandy Brocklehurst/Susan Bones. Enh. Now I'm curious as to the inner workings of the thing. I may end up writing my own anyways, so I can weight one side of the pairing just slightly towards one of the 10 or so "main" characters. (Second try: Harry Potter/Nicholas Flamel. Now that has possibilities.) [ETA: Third try: Narcissa Malfoy / Viktor Krum. We have a winner!]
The one at http://www.cyberpomo.com/randpair/ allows me some control over which groupings to choose from, but they list Cho as a "major" character, and Lupin as a minor one. Plus, they don't have dead people (like James and Lily). It does have the advantage of allowing me to rule out Dobby and Hedwig and such. Oh, apparently this is related to pairgenerator which I will now check out. My first mix: Rita Skeeter / Katie Bell / Madame Maxime / Percy Weasley / Molly -- apparently I need to go back and set it to "pair", heh. Okay, my pair is: Lucius/Alicia Spinnet. Hm, I could work with that. Third try: Maxime/McGonagall for the win!
ETA: Okay, I made my own so I could weight it properly. First I took the names of 75 characters, from the four founders to every last one of the Weasleys. (List here.) Next, I sorted by my own preference of who I'd most or least like to write in a fic. I didn't dither too much on the precise relations of each, since I figured there wasn't likely to be a lot of difference between the #26 and #27 spots (for example).
Then, I assigned relative weights by saying the #1 spot should be 5 times as likely as the #75 spot, and each successive slot should be "1" less than the slot before. Fiddling with it to make them all integers led me to a weight of 90 for the top spot (Severus Snape) and a 15 for the bottom spot (Gregory Goyle). So I want Snape's name to be in the hat 90 times, so to speak, and Goyle's 15. The total number of pips in the hat, then, is 3974. I assigned a range of numbers to each - so that 1-90 is Snape, 91-179 is Sirius Black, and so on.
In order to try it out, I took the seven sets of prompts from 7spells and picked one at random from each set, and then generated myself 7 random pairings, one for each prompt. I call it "Summer Spells." Plus, it gets me out of writing Maxime/McGonagall smut.