Do they allow mermaid tails?

Only USCG-approved devices are allowed.

No only life guard approced swim vest

You should NEVER allow mermaid tails in water! CHILDREN ARE DROWNING

Monofins

Do you mean mermaid tails as something a child would wear or the monofins you use when doing dolphin kick?

I would doubt it. I have never seen tube floats or any float things other than little arm floats on small children. You can always call and ask I suppose