For many people, the difficulty with the muscle-up is probably one of struggling with the transition from the pullup to the dip rather than a lack of either pullup or dip strength. Continuing to emphasize building more pullup and dip strength will generally have very little carryover for the muscle-up as the area in need of attention will receive little direct stimulation from either of these movements.
A simple solution to this is to simply attempt to add a small portion of the transition to the top of each pullup and the bottom of each dip:
1) For the pullups don't stress out too much about the amount of transition you successfully achieve; just be consistent and smooth in trying to add more and more of the transition to the top of the pullup rep. Eventually you will be able to end each pullup rep in a bent arm position on top of the rings.
2) For the dips simply allow yourself to slip lower then the supported bottom of the dip. Be attentive and don't allow yourself to go farther into the transition than you have the strength to press back out of. In this case "less is more" as it will allow you to more thoroughly address your weakness.
3) Once you can dip down, lower all the way through the full transition ending at a pullup top position with a false grip and return, you will for all intensive purposes have developed a full muscle-up.
4) In addition, once you have achieved a single muscle-up, you can then additionally strengthen the movement by training transitions in a row. Begining from either a dip or a pullup, get to the transition and then simply work transition "reps" by moving up and down thru the transition without ever letting your arms straighten.
Yours in Fitness,
Coach Sommer