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.