We were upthere a couple of years back, and could not find a close dog-friendly park, so we just visited on a day trip from Ballina. Their loss, as we planned 2 nights at BB, which Ballina got.
my recommendation would be dont stay in byron, go 20 k north and stay at the ferry reserve park right on the river at brunswick heads pet friendly,and much nicer.the beach has dog areas also.i know i live here.
The one oposite the sports ground near the golf course takes dogs. Their sign says no dogs but we have stayed there and there were heaps of dogs there. A nice walking track to the dog beach from the park too. About 5 ks on the Ballina side of town. I think their sign is a very old one. They were the only ones that took dogs.