Measuring sugar content of a tree
The difficult step will be getting samples of sap: have a look at the WP page for maple syrup for ideas about methods of tapping into the xylem of your trees. 

You will then need to assay sucrose in the sample of sap. There are many commercial assay kits available (Google: sucrose assay), which rely on an enzyme, invertase, to convert the sucrose to glucose + fructose. The released glucose is then measured by a glucose oxidase assay. You would need some kind of colorimeter/spectrophotometer for quantitative results but there is a visible color change, so you could probably get a rough idea of what is going on by visual comparison with a set of glucose standards.

Supplementary
An alternative would be to measure sugar concentration by refractometry: see here and here.