As fas as I know it is almost impossible to paint tiles successfully.

If you can't justify the cost of replacing the tile with laminate counters, then I think you have two options.

The most successful would be to regrout the tiles. This is not a difficult process. It does take some time, but you can easily do it yourself. Use a Dremel tool, or an awl, or whatever tool works well for you, and dig out the grout. It will take some time but it will provide you with a countertop that looks like new.

Replace the old grout with one of the new near-impervious products available and you are off to the races. It's an easy thing to do - mix the grout, pour it onto the tiles. Squeegee it around to fill in the spaces between the tiles and use a sponge to mop up the excess. Let it sit for a little while then mop it again. Let it sit some more and then wash off the grout haze.

Alternatively, you could fill the holes in with something that is close to the existing grout and then stain it with a water-based stain. If you do it a few times, you'll probably come close to achieving a consistent colour, but it's unlikely that it will be prefectly true across the entire counter.

Others on here may have some more suggestions for you. Good luck with whatever you choose.

I have regrouted tile & it's one of those most-hated jobs on my list--just below pouring cement & hanging drywall.

It is tedious; tiles will get chipped. You will get blisters & bleed.

Rather than expend the effort & expense for tools, grout, additive, sealer...I would go to Home Depot and buy from their stock of prefabbed laminate counters which, BTW, are very affordable. Installing them yourself (I did) is not difficult but they are heavy so a helper is recommended but not absolutely necessary (I didn't.)

Another alternative is wood counters. Both Lumber Liquidators & Ikea have them & they are quite reasonable. Advantage is that wood is easier to work with & lighter weight than particle board/ laminate counters. Addt'l cost in finishing supplies (tung oil/ Waterlox/ etc.)