Yes, you can do this. In fact,a latex solid stain is the product to use for this task. The trick to making this work is to use a shellac primer that will bond to both coatings.There are very good directions on how to do this on www.ehow.com . In the search box just type in "stain over latex paint".The first step
in this process will be to wipe the latex painted surface with mineral spirits. If you have problems locating the ehow website please get back in touch with me. Good luck with your project!