Painting stained exterior wood can be done but with stipulations. Follow these guide lines, in order to have the paint stick and not peel after painting over stained exterior wood.
1) The wood needs to be in good shape. This mostly applies to cracks. Any cracks not fully sealed with primer, caulking and paint will allow water behind the paint film and cause peeling.
2) Thoroughly pressure wash the wood to remove all loose and oxidized stain. This is a very important step! A cleaning solution can be used to help remove the stain. Allow the wood to dry completely before proceeding. Drying can take two or more days in humid areas.
3) Prime the wood with a high quality oil base wood primer. Two coats will work the best. Thin the first coat a little to help with penetration. Plus, the primer must be pushed into the wood with a roller or brush. If you plan on spraying, back roll the entire surface.
4) Two coats of paint will have to be applied. Allow 4 hours or more between coats. A good 100% acrylic paint with a satin sheen or even an Elastomeric paint will be the best choices.
An alternative to painting exterior stained wood is applying an acrylic solid color siding stain. When properly applied it can last a long time. Almost as long as paint, but with easier future maintenance. Pressure wash and restain verses scraping, spot priming and painting. Check with your local paint store for available products.