Dominical - on the beach across the street from Restaurante El Coco. Well maintained, lots of kids playing, and very cool two-story tree house-like play structure for climbing and viewing the beach.
Uvita - next to the soccer field and comunal salon, on the road to the Ballena National Park/Whale Tail entrance
Palmar Sur - The key feature here is the old train (playground becomes secondary!) that children can touch and play by. Also a nice park for adults, and only a couple minutes past the Palmar BM Supermercado (drop one adult off to grocery shop while the other plays with kids at this park!)
Other Kid-Friendly activities;
Manuel Antonio National Park - take a private guide, the extra $15 or so is worth it because you can travel the path at toddler speed and still see lots of great wildlife http://www.sinac.go.cr/ES/ac/acopac/pnma/Paginas/default.aspx
Alturas Wildlife Sanctuary - education/rescue/rehab/release wilfdlife program. Recommend going in the am for better attention span and cooler temps https://alturaswildlifesanctuary.org/
Vista Ballena Hotel - put the kids in the pool and enjoy a meal in the poolside restaurant. Probably the closest thing to a "date" you get with chilren ;-) https://www.vistaballenahotel.com/
Playa Ventana's dinosaur - next to the gas station and shopping/business center between Uvita and Ojochal, you can't go wrong with a giant T-Rex. A lot of the smaller animals will draw kids' attention, too. Good photo ops.
Playa Ventanas at low tide - just past the caves on the north side of the beach, shallow tide pools formed at low tide and for a few hours after. This works great for toddler/baby friendly ocean time while the cave part is fun for the adults
Uvita BM Supermercado - large, clean, well stocked grocery store good for most baby-centric purchases (e.g. diapers, formula, etc).
Mama Toucans - in Dominical, has the BEST earth-friendly diapers. Worth a drive there for them (and their granola).