Not sure it's allowed, but seems enforcement of rules is pretty lax, so doubt anyone would shut you down. My main concern would be finding a place to set it up, as the beach can get pretty crowded and the lawn area above the beach is a) extremely hot, and B) on a hill. Also not sure how you'd get power to it--I haven't seen electrical outlets there.
I agree with Daniel in general. But at the east end of the park there are some flat grassy parts that would work well up away from the beach near the pavilion. I don't know about power.
I wouldn't advise my children to play there anymore. There was a shooting there last month.
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