I saw some pictures of how someone mounted their monitor into their cocktail cabinet and thought it was neat, so I will share it with you. I can not remember who it was and do not have any photos which were posted, however, I tried to explain it below (see pic).
Basically, you route out a groove (let say 3/4") all around the cocktail cabinet walls. You then mount your monitor to a square piece of 3/4" MDF (perhaps by lowering the monitor through the square hole from the top). Finally you slide the 3/4" square into the routed out 3/4" grooves in the cabinet walls.
Make sense?