What do you mean under the term "establish"? First of all the obtained Copper/diamond interface should be examined vs the applied synthesizing process. Existence or absence interface phases should be studied, mutual diffusion of the participating elements should be examined, adhesion should be estimated. After obtaining all these results, some intermediate conclusions should be made to know how to proceed.
To create a strong interface between Cu and diamond you need a carbide forming element or at least an element with some solubility for C. This will lead to the formation of a carbide interphase between copper and diamond. You can find in my profile a number of articles on this subject. Example: we used Cu-Ti alloy as the matrix with a few % of Ti. Cu-Ti allows liquid phase sintering and the Ti forms the TiC at the interface.
First of all I agree to Mr. Kieback, you need a carbide former. Furthermore you write, that you want to do liquid phase sintering. As long as you use Cu and diamond only, it will never work. The liquid phase can only be your Cu, that means that you require a very high amount of diamond grit. Due to the fact that there is no wetting between Cu and diamond you will never receive a solid body. If you use Cu as the major component and add up to 25% (volume) you can receive solid bodies by hot pressing, but there will still not be an interface, as Cu is no carbide forming element. Kind regards Christian Kühl