Any ideas about how I can a) close the opening and/or b) attach a new adapter?
(there is a second faucet at the very bottom, so if I plug up the hole I can still use it, though not as conveniently.)

Thanks for any ideas!

A picture would be nice. It is hard to visualize from your description. When you say cemented do you mean glued with epoxy? Is the adapter a thread pipe nipple of 1/2" diameter? Is the barrel shape 1/2 of a cylinder? How wide is the top of the barrel? Aloha

> I When you say cemented do you mean glued with epoxy?
Probably cement -- barrel and adapter are plastics of some sort

> Is the adapter a thread pipe nipple of 1/2" diameter?
Yes

> Is the barrel shape 1/2 of a cylinder? How wide is the top of the barrel?
Yes -- the top is a half circle with a diameter of ~ 28-30" . The slightly recessed fill opening is a circle about 8-9"in diameter, the whole unit is over 5' tall, and the adapter is about 20" from the bottom, just enough to get a watering can under it.

If the 1/2" nipple is still sticking out of the barrel 20" up. The cut off any remaining threads and epoxy on a cap to close it. If you want to use it again, then cut of any threads, using pvc glue, slide on a pvc 1/2" coupling with slip-on side and the other side of the coupling threaded. Glue on coupling and thread in new faucet. Do you want to screen off the top hole(9" dia)or close it air tight? The barrel needs to have air to the top of the barrel to provide atmospheric pressure in the barrel above the water. The barrel produces very little water pressure so any patch or hole can be sanded and epoxied in place and will hold against the minor pressure(better done from the inside). With the barrel full there is only approx. 2.5 psi at the bottom and as the water level drops the pressure rapidly decreases. The higher outlet pipe has even less. To increase flow, increase the size(dia) of the outlets to 3/4" or bigger.