It's a bit early for rudbeckia to be blooming.
There are no birds I know that will eat unopened flower buds like that. They might go after the seeds after the plant is done blooming.
I'm almost certain it's rabbits, even if you aren't seeing droppings right there. Once they find a bunch of plants and get going, they will keep after that patch and potentially eat everything to the ground. I have a bunch in a raised bed that's a foot tall and once they found it they climbed into the bed and started chowing down.
You really are down to a choice between an ugly fence or no flowers.