Is There a Backyard Wrestling 3? No.

No. The series ended after two titles:

• Backyard Wrestling: Don't Try This at Home (2004) – PS2, Xbox, GBA
• Backyard Wrestling 2: There Goes the Neighborhood (2005) – PS2, Xbox

A GBA version of the first game exists but is a different beat-'em-up. No third installment was ever announced or released.