For North American trees, I have used annual growth rings of the wood to estimate annual changes in diameter. Many studies by North American foresters have related tree diameter to aboveground biomass via allometric scaling equations, so you can estimate annual changes in biomass. The usefulness of this approach to you will depend on at least two things about the tree species of concern:

1) how easily it is to measure annual growth in these trees (if the trees do not experience significant seasonality, cores may not have distinctive rings) and

2) whether allometric scaling equations have been developed for these tree species.

Thank you Drs Peter Weishampel & Cate Macinnis-Ng. I am working on trees in tropics. Most of the trees are exotic species, originated in South America or Africa, Asia and Australia. There are few indigenous species too. None of them show growth rings. And yes, I am interested in both - amount of carbon taken by trees and amount of carbon stored by them.

Just to give you few examples -

Delonix regia, Spathodea campanulata, Kigelia africana, Tabebuia pallida,

Indigenous - Azadiracta indica, Mangifera indica, Spondias pinnata, Lannea grandis

etc...