I saw a manual on ResearchGate of the type described by Abdelwahab Bessaad. There were graphics and regressions for each of some various types of trees regarding allometry. Unfortunately, it appeared that they had misunderstood heteroscedasticity and had printed some incorrect regression lines on the graphs. I tried to explain it to them, but I don't know that they ever made any changes.
Anyway, as Abdelwahab Bessaad said, these allometric equations are by category, and they do vary by tree, thus regression is used, but since you would be looking at a lot of trees, relatively speaking, variance would be a smaller problem than for an individual tree.
I assume you will use tree count and diameters to estimate tree biomass. You will find many papers on estimation functions (allometric biomass functions). You can also estimate tree volume first and then multiply volume with density to obtain biomass. The final step is to multiply biomass with carbon fraction (usually around 50%). I suggest you follow the procedure that is commonly used in your country/region (for instance used by the National Forest Inventory). Some of my papers could be useful for your task.