What is medium to you? Live oaks have that same spreading canopy and are evergreen (actually they aren't, they drop their leaves in the spring as the new leaves come out...)

A pollinated avocado would also drop fruit on the court. But continuing to look around for existing trees in your local area that appear to fit the bill should turn something up. Try any arboreta or botanic gardens near there for concentrations of labeled specimens.

Thanks, both -- I went to two nurseries and asked this question and was recommended an English laurel (which I can't find photos of in this form) or Bay leaf Saratoga (which I also can't photos of in this form). The english laurel seems like it would be too small...