What brand of paint are you using? And what kind of brushes?
I know everyone prefers an airbrush and it is pretty much the only way to achieve a "perfect" FBR, but it is possible to get decent results with paintbrushes and makeup sponges. Even with tricky colours such as white and yellow!
I tend to repeat the same things whenever someone asks about painting but here are my best tips:
1. Prime your bait. Gesso is fantastic stuff, it leaves a slightly rough base for your paint to stick to and reduce the number of coats needed for an opaque finish. Especially if your paint colour is lighter than the pony's original colour.
2. I use a fan shaped brush, size 4, for all my FBRs. There may be differences in the softness and quality of brushes, you'll want a brush soft enough but one whose bristles don't pull apart when you wet it (my bigger fan shaped brush does this... doesn't work at all!). You might need to get a couple of different sizes and experiment. Many also recommend makeup sponges; I have no experience with them but you'll have to see what works best for you.
3. Alternate with thicker and watered-down paint. Sometimes it's useful to do a couple of coats with well thinned, running paint that will go into the creases and lines left by the paintbrush. Sometimes it helps to focus on the problem areas and dry-brush some thicker paint to fill the creases. The more coats, the better the result. I'm usually somewhat happy after 7-8 coats and lose my patience after that.
4. You can use very fine sandpaper (600-1000) between the coats to smoothen out any bumps. Generally, sanding only works with colours that don't turn darker or lighter when they dry. There may also be differences between brands - I noticed my artist grade acrylics don't take sanding well but with most Folk Art colours it works just fine.
Hope this will help, even if a little! With handpainting you have to accept the fact that the finish will always have some sort of texture to it. Personally, I don't mind texture as long as there are no clear brush strokes to be seen, I don't want the viewer to be able to tell the direction of my strokes from the finished product.
I definitely see improvement in my FBRs over the years but I'm still fighting to produce "the perfect one". I'll probably never get there, haha. But I'm stubborn and will continue trying.