It seems to me that since the tenant has notified the landlord of the hazard, that action alone eliminates the liability. He can't claim that he doesn't know about it, can he? It is not incumbent upon a landlord to eliminate all risks, only those that have been deemed unusual or unacceptable to the general population.
Stairs, for example, are responsible for many more falls that anything that falls off of trees, yet no one would suggest eliminating them. Fixing, modifying, or eliminating non-standard features, yes, but they are too much a part of our world to claim that they are a liability to eliminate.
Fruit on trees is just the same; you can't expect ANY kind of tree to not produce a fruit of some sort that might be construed to be a hazard, and I don't think the courts will be willing to set a precedent that every landlord in the country has to cut down trees on the whim of the tenent. That's not very "green" I'd send him a notice that he is responsible for the cleanup if he wishes to utilize that portion of the yard. I'll bet the tenent has to mow the yard, anyway, and that suggests that HE is responsible for all the grounds maintenance, much like vacuuming the floor or cleaning the toilet. Tell him to get to work, and start living up to the rental agreement. I'll bet he shuts up about the nuts.
I'd look for a new tenant, too.
Post script: My understanding is that coconuts are considered a liability if they are not eliminated from the tree or the drop zone is not protected in some fashion. Of course, a falling coconut can kill an unwary pedestrian, too.