Alex,
How are you presenting it to the potential sponsors? You'll have more luck if you have a professional presentation ready, can give them reasons to sponsor - what's in it for them - especially if they are out of the pool mainstream.
One year I was able to wangle a sponsorship from an energy drink company pointing out to them that they had been mentioned on a pool forum (AZB if I recall correctly) as a great product for players. They came up with some cash if we made them the presenting sponsor (The Va State 9 Ball Championships presented by 5 Hour Energy Drink) and gave us a bunch of product and t shirts. We plastered their logo all over the place, set up a table with products, made up bags for all the players and it really added to the event.
Check into local car dealerships, hotels, bars, etc and see who would want to sponsor. A local bar, even if the tournament isn't being held there, may have some interest particularly if they have tables.
Most important thing is to provide them with some incentive for sponsoring.
Just my 2 cents.
Brian in VA