Your be glad to hear the Coventry Airport is very easy to get to though there is not really houses directly around it.
I would recommend staying in the Earlsdon area of Coventry. It is a short 5 minute drive from the airport (directly down a dual carraigeway) also I think you can get the bus there aswell.
Unfortunately I dont have any contacts for you though I would check out some of the landlords advertising to students, you may get lucky.
Prices, Earlsdon is considered the 'better' area of Coventry, though to me it all looks the same and I never had a problem there. For students of the university, 4 bed house shared - the going rate seems to be about £62-65 a week now, obviously without any bills included.
You may be able to rent out a cheap studio flat but expect to pay more!
If you want some Estate agents numbers let me know.