What is the best paint for the concrete pool deck?

You will have to strip the existing paint for proper coverage.Tey citristrip a safe nontoxic remover,Use a exterior concrete paint or stain

You could just stain it with concrete stain finishes. Many colors available.

There are a lot of retailers that sell pool deck paint especially for this project. One of them is Behr paint sold by Home Depot. Another can be ordered from the following website:

www.seal-krete.com/pool-deck-paints-coatings.html

You can paint or you can stain concrete and get different effects, and even do stenciling for a design, here are some links to check out:

https://www.doityourself.com/stry/how-to-paint-your-concrete-patio

https://www.familyhandyman.com/patio/renew-your-concrete-patio/view-all/

https://lollyjane.com/painted-concrete-patio-tutorial/

https://abeautifulmess.com/2016/08/painted-patio-tile-diy.html

https://www.thegardenglove.com/diy-project-how-to-stain-a-concrete-patio/

http://diycozyhome.com/how-to-score-and-stain-concrete-so-it-looks-like-wood/

Get paint recommendations from paint supplier. You could use a "porch& deck" paint up to an epoxy paint. You cost will vary. However, us a pressure washer to fully clean the surface. Try to keep chips from getting into the water.

If the picture is of your pool deck it looks like the existing finish should be taken off, then a new one applied. I had my kool decking painted after hail chipped it in places but am not happy with the results. Kool deck is made to keep the deck from getting so hot that it is uncomfortable to walk on. By painting over the kool deck you take away the ability of the kool deck to do what it is intended to do, and it will be uncomfortably hot when you walk on the deck. Hiring pros will probably be expensive, but might be worth it in the long run.

However, if you want to paint it yourself make sure you have no loose paint or kool deck the patio, and that you prep it properly and use a good primer before you paint. The people I hired to paint apparently did not use a primer and I have paint coming off the concrete in places. Wherever you purchase your paint they should be able to tell you what products to use and how to use them. If you can take pictures of various areas of your deck to show them what the existing deck looks like you will be able to get better advice on how to proceed.

You should take off what is on there. I would stain, not paint or leave natural. Dog's nails will tear up paint and you'll be painting every year.