Check this out:
http://www.rafflesoft.com/demoraffle/home/index.php.
It's a raffle site geared toward non-profits. Participants can choose what they want to go for and how much they want to bid. The website takes care of all the logistics and fairness of the results.
It costs $600 a year, but it fits exactly what we're looking for.
Sponsors can give away stuff. There is a project description where we could say what the Kiva Raffle is all about, where the money goes. It even has an online profile very similar to Kiva's simple style.
We could display the results something like this:
http://www.illinoislottery.com/Raffle/3-2007_raffle.htm.
If this is marketed well, this could really turn into something. If Kiva threw me the startup cash, I'd even volunteer myself to be the administrator.