The answer to this question is presumably dependent on the athlete. In our four week muscle up program, we program athletes to pulling strength or pushing strength at least 3 times a week. The goal with this regiment is to achieve 1-5 strict muscle ups. Each session shouldn't take more than 15-20 minutes, and can easily be done at the end of your workout as a cash out before you leave.
As you can assume by our program, volume is not necessary when doing pull-ups and dips. Over the course of a week, we ask you to do 60 minutes of work, at most. So if you stray away from our program, there's no need to get fancy and creative: keep it quick, simple and challenging. For example, one max out set of rings rows, pull-ups or dips.
The ideal amount of working days in this program is 3 to 4. Keep in mind, lactic acid build up (a.k.a. soreness) does not affect your strength! Your muscles do not run off lactate acid; so if you are thinking of skipping a day due to soreness, that doesn't always have to be the case. However, keep the volume low to avoid overuse, injuries and excessive breakdown.