Here are two good possibilities:

Spare Air

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This is used as a small emergency bottle to get an out of air scuba diver to the surface. In a pool, it would last long enough to fulfill some Merfantasies. NB: You must be scuba certified to even purchase one of these, let alone get it filled (which could be done from a scuba tank).

Pony Tank

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"Pony" tanks are often used as a larger emergency air source for a deep dive. A small tank like this (perhaps a smaller one) could be strapped across the small of your back (horizontally), as well.

So, what do you think..? This diver is willing to experiment!