Start by asking the business owner for a 10 minute phone call in order to ask them a few questions. This is a low threshold way of getting them to say yes. Many times, if your questions are interesting, they'll spend 30 minutes or more with you.

I actually pre-sold copies of my book in order to pay for the inital setup and printing costs. Here's my suggestion:
1) Create a list of people you'll invite to the raffle
2) Don't just email people, call them to get them excited about the raffle and ask if they'd participate
3) Have a compelling business story or story behind the raffle
4) If the prize can be a holiday gift, that would be ideal since many people need gifts for co-workers, the mailman, and other nonfamily members.

Feel free to call me if you'd like to discuss the strategy further.