How would you cover a paneled wall that has been painted?

What is your goal? Maybe I am not understanding your question. Are you talking about walls or an island?

For a paneled wall that has been painted, you can repaint in the color of your choice, wallpaper, peel and stick tile, stencil to name a few.

Or you removed the island revealing the original paneling while the rest had been painted over? If that is the case, just repaint. Will take a little extra prep work on the original paneled wall portion, but certainly doable. Wash, repair, prime, paint.

If you are saying your demolition exposed and unpainted portion of the wall and you dont have the original paint. I would simply scrape a bit of the paint off in an unobtrusive area, take to a paint store that has computer matching to get a match. Just note down if its flat paint, or satin, semi-gloss or enamel.

You could put different paneling up or repaint whatever color you want.

I think I would just repaint the entire wall. Try to get the color as close to original or go with a completely different color, something complimentary. Wishing you well.

I agree with Sharon, any paint or hardware store can match your old color. Sand the edges where the peninsula was and prep the entire wall and repaint. Alj is also right in suggesting that now would be a good time if you want to change colors. Please post a before and after when you are finished. Good luck!