Based on THIS fanfic, though I have read it long ago, and didn't try to retell the story exactly.

Even with one sex per male every 8 days, and with merely 60% intercourses ending with a (single-kid) pregnancy, the population would be stable.
(I even made the pessimistic assumption that the average lifespan is 75 years, even though long-living Earth Ponies would skew that lifespan upward by quite a bit.)
(Shorter life = deaths are more frequent = more sex needed for the population to be stable.)
(I also assumed the reproductive age as 13-50, which excludes about 50% of males as sex partners.)

If you excluded (N-1)/N of males due to cherry-picking, they would have to have N times more weekly sex than initially.

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For population to be stable, number of deaths must equal the number of births. If people live 75 years on average, then a randomly-chosen person will die today with probability of 1/(75*365) = 1/27375, assuming unbiased random sampling that is as likely to pick a newborn as a person who's exactly 80 years old.

Multiply that fraction by population to see how many people die (and need to be born) daily.

And also that fraction equals (NumberOfReproductiveMales/SizeOfWholePopulation) needed for 1 daily-intercourse-per-male to keep the population stable. (Assuming 100% pregnancy success and 1 kid per pregnancy.)