I maintain that wood density is critical to wood utilisation and can be measured indirectly using tools such as the Pilodyn in both trees and lumber. Even systems like densitometry and SilviScan give accurate a data for specific samples, but are actually indirect as far as trees and logs are concerned because they only measure a small volume. I consider measure from standing tree increment cores to be the best way to estimate log and stem density, using algorithms to link cores to the portion of interest.
For indirectely estimating wood density in standing trees you can use a Pilodyn, as pointed out by DJ Cown, or a Resistograph (see pdf below). You can also remove a increment core from the trees and use densitometry or Silviscan to analyse the wood (as suggested by DJ Cown), and even use Near Infrared (NIR) Spectroscopy for estimating the wood density. For NIR spectroscopy approach, check the paper indicated below.
Other possibility is to apply micro-drilling technique, according the force during the drill it will be possible to estimate the density......Just check the micro-drilling....
I confirm the information given by Vladimirs. I'm using micro-drilling on wood. Based on applied load on bit and torque while drilling, it is possible to assess some properties of the wood such as density.