Let me temper GeoPaveTraffic's suggestion with the caution that 3" Shelbys may work well, or be be a wasted effort, depending on the soils involved. If the material is plastic, or is partially saturated and has enough fines for capillarity to hold it together, it may work. A non-plastic saturated material is likely to be trouble, as is anything with more than a trace of gravel. In such cases, you may need to go to an Osterberg or other piston sampler, larger diameter dry coring, etc. Loose, saturated, non-plastic materials are the worst because they want to densify at the least suggestion of disturbance, and you end up with free water in the top of the tube. In extreme cases, where the material is loose, saturated SP, and the density needed to be known very precisely, people have even frozen the ground with liquid nitrogen and cored the frozen soil. (I'm not making this up. As I recall it was for a power plant, maybe nuclear, in Japan.)
On the other hand, if you have plastic clay that you know to saturated, you can get a pretty decent density from water content and Sp Gr.
Why do you need to know the density more precisely than you can get from correlations? Also, what materials are you dealing with?