Yes there are quite a number of car rental places in Jamaica that do not require credit card deposit,I know people that use them some of them are Jamaicans and some tourists both not having used a credit card.
The 250 usd deposit is just incase the car is not brought back on time it will not be touched for damages if the nil liability insurance is paid for.
Thanks ohliz for all the little extra bits of advice and wrtiii and beachgirl they are definately other options to consider which you have suggested.