How do I paint mahogany furniture?

Mahogany is a beautiful wood, unless it's damaged, I would try to refinish it.

Take a good photo of the item to the paint department of the home improvement store and ask them what will work for you. They have the best selection, the most up-to-date materials and most important, the most informative sales staff to get you what you need for a professional job and can help figure out what is going on.

If you must. Wash down with TSP and then sand the sheen off and prime with Oil based primer

Then paint with oil based paint.

You'll need to use a stain blocking primer on the mahogany wood. I have had great results with General Finishes Stain Blocker, Dixie Belle's BOSS, and BIN Shellac based primer. All work really well.

Then you can follow this post to get all the details on how to paint furniture in general, with some info on how to prevent bleedthrough. https://www.arayofsunlight.com/2018/11/how-to-paint-furniture.html

You'll need to use a stain blocking primer to get the job done no matter what kind of paint you'd like to use. Here's a good article on stain blocking: https://rootsandwingsfurniture.com/blog/stainblocker/