Is it illegal to have a trampoline at the beach?

If it isn't, it should be.

I assume you are asking if it is legal for you to bring your personal trampoline to the beach. This would depend on the regulations at the specific beach. In California, each city has rules that control its beaches. There are also county rules and state rules. Some of the rules are posted online if you google. Most beaches have rules about trash, dogs, glass, alcohol, and bonfires. Smoking is not allowed on any beach. Some counties have rules against throwing a frisbee or ball on the beach as well as against digging deep holes. Considering that a trampoline is, by its very, nature dangerous, and considering it would need to be weighed or anchored down, most likely no beach will allow it, or not for very long. Beaches most likely do not have any rule specifically against a trampoline, since it would be rare for one to be brought. However, if you show up with a trampoline, you may be told to remove it. Also, it seems like placing a trampoline on a shifting surface like sand would greatly increase the danger.

What does the City ordinance say? Since you don't tell me what beach, or what state... how can I possibly know!!!

That would depend on whether the beach was public or private. I would assume that the owner of a private beach would control the use of the trampoline and take on the liability if injuries occurred. It's probably not permitted at a public beach for several reasons, including the liability issue.

"Illegal", probably not, but if the beach has rules against that sort of thing, they can prohibit someone from setting one up.

My guess would be that you ought to check with the town clerk at the town hall or the police dept. I would think not, but trampolines are dangerous and it might be that the town has some regulations concerning them.