When my mother had her store, people would often come by asking for team sponsors. They would go to door of small businesses. Since times are tough for all, she preferred when she could co-sponsor. I would recommend making a flyer that has all info and talking to as many owners as possible. You should get a few donors. Then, comes the important part: Thank You's, including encouraging the tennis team members to thank them too. To get repeat sponsors, they must feel appreciated. Patronizing their business helps too. Good luck pounding the pavement.
I'll sponsor you. I am president of: The_Doctor Incorporated. Concerning the level and amazing talent off the highschool tennis team.. we are offering you a $0.25 dollar contract? Or should I say "cent" contract.
You can seek sponsorship from groups like USTA and PSAL. These are organizations which sponsor students' athletics in public schools. These groups organize tournaments for various schools around different schools