I have an older birdbath/fountain that I wish to restore. I have no idea as to the origin. It is very heavy, well built, and in generally good condition. The one item for which I cannot find any type of replacement is the umbrella as seen below. It seems to be made of fiberglass. I thought of taking it to a boat repair shop to see if the fiberglass could be repaired, but perhaps someone knows of a source for a new one.
You may be able to glue the pieces but it may/would be a difficult job to make a holder to keep it together while the glue hardens. From your photo it appears there is a large piece missing or do you have that piece?
You do not give the measurements of the umbrella but it looks fairly large and is probably heavy (it seems the fountain might be made of concrete?). If you have a boat building company or a repair shop in your area, they might give you some suggestions and they might even do a repair but it would probably be expensive. This style fountain is a well liked item and generally sells for quite a few bucks but if you could locate a local dealer or especially someone who makes this type fountain they might make you an umbrella.
You can try Google with something like - where to buy concrete water fountain -with your zip code and you may find some dealers/stores in your area or close by.
Here are a couple of interesting sites:
I would try Gorilla Glue.
I wonder if someone who works in HVAC could make you one (they make and bend the metal to make duct work). It would not be fiberglass, but a light weight stainless.
I had the same problem-im bought a clay pot large enough to fit my umbrella and turned it upside down-market it same color as fountain and it worked beautifully. (It already had the hole for my fountain pipe to fit in)