if in deed it is a concrete fountain fist thing does it have cracks in it or is it just leaking if there are no visible cracks you can get a sealer that will stop the leaks that way if it is cracked then you need to get a bonding agent that will fill and seal with out expanding then seal it over in a color so it all matches

Get a concrete filler from your hardware center.paste smoothly over the inside of birdbath. If your not sure ask. Also pays to paint poly -urethane over concrete. Make sure it all dries properly before filliing. I believe there is a non toxic filling agent you can use,but none of our birds have died yet.The other way is just to put plastic bag of the right size in bath,and replace when neccessary.

buy a bag of grout mix at the hardware store(usually around two bucks) clean the inner bowl of the bird bath. Mix a small portion of the grout per the instructions on the bag. rub a 1/4 inch layer across and covering the interior of the bowl. Allow to set (two days) Then it should hold water with no leaking.

There is something like liquid cement you can buy. I used it to fix a hole in a bathroom pipe. It comes in a tube (like caulking)and you just cover the hole or crack with it and let it dry. You will need to keep water out of it while drying of course but it is very effective.

Go to Home Depot, ask the man there for a concrete repair: A tube of this and a caulking gun, maybe you can borrow the gun from a friend.

I used silcone caulk inside the bowl. Won't last forever, but it's a cheap fix.