Ask Mr. Smarty Plants

It doesn’t look good for your quest.  Eugenia is a genus and there are 32 different species of it. The tough part for your quest is that a characteristic of the genus is a centimeter sized cherry-like fruit.

  I’m guessing you are considering a Eugenia apiculata [Shortleaf Stopper], which is present in California as an introduced species rather than as the native species which Mr SmartyPlants recommends.  The USDA shows multiple species of Eugenia in Florida, Puerto Rico, and the Virgin Islands  but even then, mostly as introduced species. Eugenia axillaris (White stopper) is the only one native to Florida.   From the pictures it looks like all of them have berries, so it doesn’t look good for finding a nice clean, native Eugenia bush.

  How about another Myrtle that is native to California?    Morella californica (California wax myrtle)  is an evergreen shrub or small tree native to the Pacific Ocean coast.  It is on the recommended species list for southern California.  That would be the preferred native.

 On the other hand, on the species record for it’s near relative, Morella cerifera (Wax myrtle) it was noted “Because there are separate male and female plants, if you want berries you must have male plants close enough to the berry-producing female plants for pollination to occur.”   This might be your chance to keep a clean sidewalk!  Unfortunately, It seems that Morella californica, California wax myrtles, unlike Morella cerifera, are monoecious, i.e., they have both male and female flowers on the same plant and thus all shrubs will produce berries. If you would like to dig deeper into this, here is a scholarly reference that discusses their fruiting.

As long as you are considering trees other than the Eugenia, you might consider Cercocarpus montanus (Alderleaf mountain mahogany).  It is evergreen and doesn't have berries.   Here's another possibility, Ceanothus megacarpus (Big-pod buckbrush) or one of the other Ceanothus spp.   I think most of the California ones are evergreen and don't have berries. 

It would be a good idea to contact your local extension office; here is the website for the LA County Extension office.  The experts there [master gardeners] should have opinions as to whether this approach can work for trees that do well in your area.