I think what you may have heard of is frequent pruning causing these to become diseased through the wounding that occurs when that is done. So, you would avoid lots of canker formation by not pruning so much.

If you have a specific canker disease you know to be prevalent there seek guidance from California Cooperative Extension.

Japanese flowering cherries sold on dwarfing rootstocks are on the market up here, perhaps that is the route you should have taken. Otherwise planting fewer of the trees probably could have prevented your presently developing concern.

Thanks bboy for the advice. Just to clarify, pruning risks cancker even in the Spring. Light pruning or no pruning is your recommendation. Although these trees are planted close together, by that I mean about 10-12 feet apart. BTW are there some species of flowering Japanese cherries that are more resistant to disease problems than others?

I think Lake County nursery in Ohio has claimed their new Pink Snow Showers weeping cherry is less problematic. It popped right away in a garden center here so you should be able to get it somewhere soon, if you want to try it.