What Type coolant does it use? R12, R22, R134A? Is it completely depresurized? if so you need to find the leak and repair first, then have it vacuum pumped to remove the non compressable air, then recharged. if it is just run down through slow seal leakage over several years , you might be able to recharge yourself with a bottle of coolant and the valve kit from pep boys or walmart. .
I would think any of the local refrigerator repair shops could do it. there's a maytag shop near you. or there are some listed under AIR CONDITIONING EQUIP.-REPAIR in the yellow pages. bill vandervort appliance repair looks promising. or an auto AC repair shop. all have the vacuum and recharge equipment. but the appliance places might have repair parts. Check also under yellow page ads for APPLIANCES-MAJOR REPAIR. I haven't any personal experience with any for repairs. but it seems like there are lots of repair places. it's just a mini fridge unit.