View photos of the edible (barely) plant, Forestiera pubescens (Desert olive), profiled in Wild Edible Plants of New Mexico.

A passage from Wild Edible Plants of New Mexico:

I’m not going to exaggerate and make Desert olive into something that it is not. It’s one of the more bitter–tasting (but still edible) berries in New Mexico. The key to eating more than one or two berries is quantity. If you can get past a small handful, you’ll find their taste less overpowering.