Do you mean the spotted wing fruit fly, aka SWD?

If so check this info
http://groups.hort.oregonstate.edu/group/spotted-wing-drosophila

Here is a link that might be useful: uh oh; spotted wing fruit fly

I'm not sure what it is. From a conversation I had with the city, I understand that the fruit fly is tiny and lays eggs in the fruit - then the larvae drop and burrow in the ground. They suggested getting chickens - not a good solution with a Schnauzer! Even the birds don't eat the fruit once it's affected... by the time the fruit is ripe it's all gone bad.

My neighborhood has them and they truly are vile little things!!! Nothing like white maggots in all your cherries, ugh!
Here is UC Davis' sheet on things that might control them--at least there is some hope.

Carla in Sac

Here is a link that might be useful: http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn74158.html

I'm asking about natural predators because the management solutions are not practical for me. The tree is large so spraying and/or netting is out of the question.

Read the info on the SWD site that I suggested. For one thing, you can "cage" individual branches. Yes, I know that sounds goofy. But it's up to you to decide how you'll proceed.

At this time, lots of luck with finding predators. Currently the key to management in a home garden is a combo of strategies which includes trapping, sanitation, and prompt harvesting.

To return to the predator question -- none are known at this time.