On a recent "field trip" I noticed the prominent rings that palm trees have where leaves were attached. Can you tell how old it is from these?
This dendrochronologist says that some people extrapolate the age of palms from their leaf scars, and the time it takes to grow a leaf, but that the method is just a wild guess. But there is no other method that can be used intrinsic to the palm i.e. you can't count rings, and you can not carbon date.