I will be shocked if you can find a car or booster seat for less than $9-$10 per day. We have always paid at least that.
One thing you can try is renting a minivan that already has carseats built in. We rented once from Thrifty and the car seat was part of the van. That way it didn't cost us extra, and you don't have to worry about the seat being dirty.
Not sure what rental cos. offer this but a quick call or e-mail and they'll tell you.