I was reading about birdbaths in the New York Times (warning: paywall). TL;DR a heavy, shallow bird bath is good, near a hose so you can wash it and fill it up regularly and easily.
I was wondering about how to make a stone birdbath, rather than buying yet more concrete, and it is quite doable. This is the first video I found, on This Old House. The bit I’m interested in this bath itself, not the stand, so fast forward to 5'50".
Now to find a friendly, local stone mason…