What paint or stain colors can I put over navy blue on furniture?

Stain will not cover paint.

Chalk paint of latex will cover it. Chalk paint will not need prep work unless it is a glossy surface you are covering. Latex may need to be sanded lightly as well if it is glossy.

Stain is really not going to adhere to painted furniture. Stain is meant to soak into wood but on painted furniture it will just dry on top of the paint and can wash off. If you are trying to darken your painted furniture you can use a dark wax or a glaze. If you want to repaint your furniture you can either use a chalk paint and a little bit of prep work or prime first with a primer and then use a different color latex paint.

Here are some tips for using glaze over painted furniture. This might help you Pat. I am assuming you want your navy blue furniture to be toned down. The glaze will help that. You don't mention what kind of paint you have on your furniture. Is it a factory finish or something you have painted yourself. If you painted it yourself what kind of paint did you use? Give us a bit more information to get some really specific answers for your situation!

http://gypsymagpie.com/2017/02/tips-tricks-applying-glaze-furniture.html

The best thing is to prime first. I recommend either Kilz or Bullseye 1-2-3. I covered red in one coat of Bullseye primer.