As for my knowledge goes age determination of wood core sample in diffused porous wood is difficult. The best available method as on today is carbon dating only.
I think that would be challenging, but depending ont he situation, might be possible. Can you tell us anything more about the sample - could you look at its stratigraphic situation and date it by its context? Has it been treated in any way, such that you could date its treatment? Is it big? Is it small? How precisely do you need to date it? What is its condition, and how old do you expect it to be? Why is carbon dating not an option? I know this is a lot of questions in response to a question, but it can help narrow down options.
The sample was obtained from a well, so it was submerged for quite a long time. Carbon dating technique is out of question as technology is not available with us. So it will be the last resort. Before that i wanted to whether there are any other means to determine the age ( approximate determination might do good).
Ok, carbon dating would certainly be best. The stratigraphy of sediments in the well might have yielded clues, but I am guessing it is now too disturbed to be of help. I hate to say it, but I think carbon dating might be your best solution, as any other radiometric method would at least as expensive if not more, and probably less useful. Dendrochronology could also work, but I understand you have ruled that out as well.