I use Bullsyee or Kilz before I paint such areas. I just painted my garden shed door today which was stained in oak. Before painting it, I gave it a good coat of Kilz or Bullseye, not sure which one I had on hand at the time. A few hours later, I painted it with the exterior enamel. I think the Kilz makes it bond better with your aforementioned stain.

Do a test door first. I think you may have to do more than that. The house we purchased had paint over stain on all woodwork and it's all peeling off. I tried sanding the loose stuff off and basically ended up stripping the entire door frame...then kilz, then repainted. I spent hours on just one door/frame and am considering replacing all woodwork (4500 sq ft home.) It's a nightmare. I've just bought a heat gun and will try that.

Anyway....to save yourself grief down the road, please do it right the first time. You may have to heavily sand it first, then kilz, then paint.

I was given the following steps, and was very very happy with the results!

Wash it. Use warm soapy water and a scrubbing sponge. Use Dirtex as choice for paint prep detergent. Wash it before you sand it!

Sand it. It must be dull. Use #180, follow with #220. Vacuum and wipe it down to remove dust.

Prime it. I prefer BM Fresh Start Acrylic primer.

Paint. When using BM, I prefer Satin Impervo. Two coats for maximum lustre and durability. If you prefer semi-gloss, the Aqua Pearl would be an excellent choice.

Hmmmm, I forgot that "wash it" part and incidentally don't use any Murphy's or pine oil in washing it and if yours was only 5 years old like mine and out in the weather, where it gets constantly rained on and not too dirty, a good washing and a coat of Kilz. I forgot that not everyone has the same conditions. ;-)