We have been to the park at Trunk Bay in St. John's two years in a row, the last time being November, 2006. We have purchased alcohol (beer) BOTH TIMES we were there. I also think that I saw rum offered there, too, but I'm positive that they do sell beer.
As for the chairs, I don't recall seeing any for rent on the beach. Everyone sat on their towels or brought their own chairs.
There is also a snack bar and gift shop. Snorkeling trail there is nice for the novice snorkeler. There is an underwater trail that you can follow that is pretty neat.
Hope this info helps.