I had similar issues with the MJZ 909 violin I just got. The pegs would keep slipping overnight and detuning it.

The trick is that you have to start to push it in from a little bit off the note (I usually do it flat) and turn the peg to the right spot at the same time you're pushing in. (You're adjusting the pitch some while you're shoving it in, for clarity.) That takes some practice. I usually missed, and had to either start over, or live with it being a little off.

My solution was to put Wittner pegs on it (Perfection Pegs also work). You don't need to worry about fine tuners after that, they hold their tuning, and on the occasions when you DO need to adust it, it's simple and easy. No pushing in or pulling out of the peg, just turn it and adjust your pitch.

That's an overly expensive solution for some people (for a viola, I believe the Wittners are $95), but I figure it's a a one-time cost, and it solves a whole bunch of problems, and solves them well.  Only downside is that when putting on new strings, you have to turn and turn (and turn and turn and turn....) to get the string on.

One bit of advice about putting those on. You'll probably have to use a reamer if you do it yourself, and if you do, be VERY cautious about how much you cut.  I thought I was being cautious, and ended up overdrilling the E string peg holes. Only by a hair, fortunately, but considering I thought I would only be about a third of the way done, finding out I was about .5 mm too far in was a nasty shock.  Practicing on a beater violin/viola would be a good idea, if you have one.