CP,
I'd try to get the town to let me shoot a rifle. If they won't(high probability),you'll have to try and make do with what you have.
I think I would set-up as many tree-stands as possible,trying to border the park. I'm saying tree-stands,because I think they would give you the largest viewing area. Our eastern coyotes are well known for hanging up in the brush and carefully checking out whatever attracts them. An electronic caller would be the ideal for tree stand hunting. Your able to keep the sound on the ground where it belongs,and away from you. They are an investment,$200. and up,up,up.
Can you hunt in the park?
As early as you can,and the last hour of the day will be best.
I'm sure coyotes with a bow will not be easy. I don't bow hunt,but I have called coyotes in well within bow range.
Like I said,looks like you'll have to make do with what you have.Or do nothing.
Have you called the state/town ADC agent?
I can't speak for the whole state as far as bobcats go,I live way up near the top.But up here,I would not say the cat hunting is good.Not worth a trip up anyway,unless you are going to use dogs.
NiM