Ahaaaa!
https://birdseedandbinoculars.com/wordpress/keeping-cats-out-of-birdbaths/ I like the last one here:
https://www.bobvila.com/slideshow/wing-it-14-approaches-to-a-diy-birdbath-44300#cake-stand-bird-bathI just remembered an old shallow white quiche baking dish (dunno what it's for really) I've never used that'd make a perfect birdbath for the way-back patio. Dunno what to set it on but I'll think of something....
Your simplest answer may be a hanging birdbath. That nice tree can earn its keep!
"One DIY birdbath is an ordinary hanging planter. In the center, set in a terra cotta pot upside down and fill in around it with soil and plants. Finally, set a medium-size terra cotta plant saucer on top of the terra cotta pot, hang, fill with water, and wait for the birds to discover it." (Or you could just fill the main planter with something to take up space maybe, like used jars upside down, and fill around those with dirt. That way the only purchase/find you need is a hanging plastic planter and one saucer.) Some flat stones in the bottom of the bath give smaller birds safe footing.
If you find something metal and can drill three holes spaced around the edge, you could even make one use metal clothes hanges wire..... One thing I read suggests painting the outside with acryclic paint .... ooo, colors!
Even simpler if you can find one is a recycled galvanized garbage can lid. I read that the ideal water depth is around 2.5 inches.
Since I have no cats in the yard, I guess due to Pooch, I could set the white one on the ground, which birds also like. It's only about an inch deep but it might work, or maybe I could use that as a base bath for wee birds and add an inverted plant saucer that's a little deeper for the bigger ones.
Oh fun fun fun...
My side patio is roofless, which in summer is wonderful because the one huge tree is just behind the house (TOO close for sensible people) and I can sit and stare into the canopy for ages. Lots of bird and squirrel action. The patio is stone (irregular rejects I got from the stone yard a friend owns) and my yard guy built it for half the cost of companies and did a great job--it's beautiful). Say about 30 feet long and maybe 12' wide with the length on one side lined with stacked reclaimed railroad ties and dirt behind those. About five years back he divided all the front-yard hostas the deer were eating and moved them to the patio raised bed and now they're huge and lush all summer, safe from deer. A tall wooden property fence is behind the hostas. My neighbor's fragrant tree branches (dunno what) hang over the fence and create nice shade. The rest of the patio is open and mostly sunny (though part gets shade from the big tree) and there's a bit of grass at the back end and a corner bed young friends made of stacked cinderblock pavers, in a curve. There's enough sun for flowers and a shorter fence on the other side for no particular reason. (I just had two climbing roses put there.) I added another short fence at the end, with a gate out to the big yard. Have two big pots with cherry tomatoes on the yard side of that so I can use the fence to secure them as they grow. At the driveway edge I had the fence guy build a nice wooden enclosure for the bins, so it looks pretty welcoming. And if both gates (top of driveway and entrance to back yard) are shut, when friends bring rowdy dogs to play out back we can even close them off the patio for a while.
Incoherent description I'm sure but if we could figure out how to post pics, I would!
hugs
Hops