I used Bayer Tree and Shrub (a systemic) and the Bayer Mites and Insect spray for spiraling white fly on my Christmas Palms. It seems to work well. BUT the label says to not use it on anything that bears edible fruit or nuts. So I don't know how it would impact the coconuts - but I wouldn't take a chance.

Neem says it is safe for nuts and fruits. Maybe this is what you should try.

Is the sooty mold on the fronds, or just where the fronds connect to the trunk? My neighbor sprayed his trees (also dwarf royals) with either Bayer or Neem (I forget) and the next day hit them with his power washer. I thought sure he would take all the fronds off the tree, but he held back far enough that it was a strong spray, but not excessively so. His method controlled the whitefly and removed the sooty mold.

Again - we are battling the spiraling whitefly, but maybe this info will help you. Good luck!

Crenda, thank you for your help. The whole fronds are covered with the sooty mold.

I'm going to try your neighbors approch with neem oil, then rinse. I just ordered a hose end sprayer Gilmour 362 that is supposed to be strong enough to reach the top of my tree.

I just discovered whitefly on my Christmas Palm. Had not encountered it here in FL before, but had it bad on my dozens of hibiscus plants in SoCal.
I never got around to applying neem, but I did just spray hard with the hose from underneath every single day until they were gone.