You might want to consider planting Sapodilla tree. The fruits don't seem to attract any birds or squirrels or rats. Also, the fruits don't look attractive when mature and I don't think most people recognize them either.
Besides, the tree is good looking, easy to grow, evergreen, not disease prone and partial sun ok. (my personal experience from growing it since 2015 in my yard).
Others may suggest differently, I am pretty sure. Good luck with your search...