Can I paint over veneer finish

You can if you use a really good primer that is made for adhesion so that your paint will stick. Or you can paint them with chalk paint, which requires less prep and is made to stick to surfaces, but I would still lightly sand and maybe do a primer first.

Yes, you should prime your laminate furniture first before painting is simple. Laminate has a shiny finish and if you just try to paint directly on it, the paint will not adhere well and you'll visibly see the paint bubble up as soon as you apply it. I've made this mistake. The solution is primer, it will adhere to the laminate, and it will create a surface for your paint to stick to. It will keep your paint from scratching or peeling off, it will cover up the wood stain, and it will even cover up that musty smell old furniture tends to have. Basically, primer is awesome. The primer I usually use is like Kilz, and it works really well. Just look for a primer that says it's good for adhesion.

Hi Gladys. Yes you can paint them. I would prime them first with a oil based primer. It is more expensive but works better with varnish. Then paint.

https://www.doityourself.com/stry/how-to-paint-over-a-veneer-finish

You need to break or disturb the surface of any laminate. Easiest way to do that is a light sanding. Follow that with a good primer and a few coats of paint. The sheen is up to what you like. I once painted a laminate dresser without first sanding and the paint ended up peeling off.

Hi Gladys, Here's a video that may help: https://www.youtube.com/watch?v=S3qDfPhUQ5Y

Have fun!

You sure can!

Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 120- to 220-grit sandpaper. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like Zinsser 123, KILZ,or BIN and have it tinted to the color of the top coat. This will prevent dark or stained surfaces from showing through the top coat. Acrylic, or water-base, paints are low-fume and clean up easily with water. Alkyd, or oil-base, paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.