Robert,
You may have thought of this before, if so, disregard.
How about a 'donation' of $10 (or $20, whatever it takes...) gets the member one chance in a raffle. The more you donate, the more chances you get. At the end of the month (or two months, whatever...) all the chances get thrown into a hat. Draw one and he's the winner. Start the cycle over for the next raffle.
The prizes might have to start out small, but once some revenue flows in they could get bigger.
Maybe this is how your giveaways already work, but I'm under the impression everyone is eligible, donor or not. This method might encourage more to be donors.