You're looking for 'hosted mining' - you'll have more success looking for those terms.
I haven't used any, but this popped past a few days back:
https://bitcointalk.org/index.php?topic=973069.msg10636866#msg10636866Not sure if he's taking on new miners, but give him a poke

There's also a reasonably well-maintained list:
https://bitcointalk.org/index.php?topic=622998.0that person to do the minning til I profit and then we share profits.
That might be a dealbreaker, but that depends on exactly what you mean by that

Typical hosting solutions just involve you paying (up front) a fixed fee for hosting+electricity+maintenance and some incidental fees (installation, additional services required). If you do profit, it's all yours. If you don't, they still get their normal fee - meaning very little financial risk for them (other than insurance and such).