How can I change the color of these tables?

I say chalk paint them. You can find a pretty blue/gray color and simply paint it on. It's super easy to use, no prep work required.

If you do not care for the chalk paint idea,lightly sand,clean,prime,paint and seal.

I also suggest chalk paint - you can make your own which will save $. Recipes for making your own here: http://salvagedinspirations.com/best-homemade-chalk-paint-recipes/

Hi,I have recently used farrow and ball elephants breath eggshell paint for my furniture,it's a light grey colour it looks fab and is so easy to use and has a lovely smooth finish and easy to wipe down no undercoat needed if the furniture is clean.

Artijan

I used semi gloss spray paint for theses. Just wiped the down with a tacky cloth first and then painted.

I would use Satin finish paint, not as glossy as Semi-Gloss. You might consider keeping the top natural wood (can change tone with gel-stain after you sand down a bit). This is the best example of the style... https://www.wayfair.com/One-Allium-Way®-Orner-Wine-Rack-Table-OAWY6292.html

I too am planning to paint a very old bedroom set. Sanding down is very important...you must have the varnish roughed up to create a tooth to the surface for paint to stick. Be sure to use a damp cloth first, let dry, then use a tack cloth to pick up the fine particles left behind. Now you're ready to paint the furniture any colour you wish. Gor for it.

Oh I bet the set will look gorgeous painted! I agree with the others about using chalk paint. The only tricky part I see is painting the shelf area on the side tables. Be sure to have a short handled brush on hand to make it easier to reach into the tight space.