It cracked and I reapired it with 2 part epoxy, but now this year it's leaking again with no visible cracks. [/quote]
That's a tough one.
Sunlight, water, wet / dry, wet / dry conditions all work against you.
I really don't know the answer to fixing bird baths but plenty of experience with what doesn't work.
Very few paints are going to survive under water,
Resins...like fiberglas will break down in the sunlight.......etc.
This will sound crazy but what I think might work is smearing bentonite clay into the bottom of the birdbath.
Bentonite expands about 20 times it's volume and is used round the world for sealing ponds, damns, well casings, basements, and so forth.
Sprinkle some powder in, smear it around like working grease into a bearing, remove the excess and mist some water in. Keep it moist. A few hours later fill the birdbath with water.
In it's basic form it's cheap cheap cheap.
By the time it's gets to hardwares stores the price goes up.
If you have a foundry supply you might be able to sweep some off a pile on the floor.
Otherwise....you might be able to buy "expanding grout" at the hardware store.
One of downsides to using bentonite is the fact it does expand. It is used for busting large rocks apart where explosives can't be used. Drill a bunch of holes, insert bentonite and water and come back the next day and the rock is smaller.
If you have no visible cracks I'd think this solution would work good. Bentonite is not toxic, the birds would care, and I think would hold up better than many other product and you couldn't tell the difference.