I am currently making a species that inhabits mountain rivers, deep lakes (up to 2 miles deep), and wetlands. They can breathe air along with water (as long as it isn't salty). So far, i've been brainstorming hand games and sports, but am totally lost on toys. It needs to be easy to make, because this is a preindustrial society, and relatively simple, like something along the lines of a fish pulled along by a string.
/something along the lines of a fish pulled along by a string./
The kid versions would not have hooks. They would be gaily painted little fish, squid and other water creatures. Some would be pulled by strings at the end of sticks and made to swim. You could have whole schools of them. You could make them do trick swimming, like yoyo tricks. You could shoot them thru the water with elastics and compete for distance, or see if you could land them in a circle. You could trade them. You could bug the real fish with them.
In response to sonvar. I really did play with balloons. If your society has fixed structures (so not swimming in the middle of the ocean). It would make specific sense to have objects that both float up (like balloons) and fall (like most things normally).
A fair portion of toys are based on things around. Toy animals/people/plants etc. This would just be a recreation of the environment in whatever materials are at hand. Also, does your society have sports? Toys often deal with sports. I will note that throwing things is a lot harder underwater (friction is quite high).
I'd say most toys in this time period on Earth were probably cloth/wood and handmade/roughmade things. (Also sticks...) So a similar level of primitiveness (wood doesn't work too well underwater though)?
I think it would be cool to design sports around the surface of the water. There are lots of interesting interactions that can happen there. For example, use a "projectile" that falls in air, but rises underwater. Then if thrown underwater it curves up, if thrown in air it curves down.
If this is normal water, it would need a lot more aerodynamics than a ball, think torpedo like. Depending on how much you want to wave friction, make a material that could bounce above and below water in a diminishing sine wave for fun.
At heart, much of play is mimickry
A broad range of kids toys are designed to mimic or simulate the things they see adults doing- fashion dolls, toy cars, play kitchens and tools, dress-up clothes, baby dolls and BB guns are all ways to play out the lives they see (or imagine) their parents and the adults around them living.
...so if you know what your adults are doing, you'll know what their kids want to do
Look at the tools and roles parents, the authority figures in their lives and their cultural heroes have- the kids will almost certainly have toys that mimic those. If the adults herd fish while riding seahorses, for example, their kids will have a seahorse head of woven kelp on a stick they'll swim around with while throwing nets over carved wooden fish. If babies in this culture are hatched from eggs, kids will have play eggs in a play nest they can "tend" to.
It depends on the type of survival skills of the specific race.
Games are part of the survival skill training, which includes copying what they see their parents doing. A race of herbivores which have lots of prey hunting them would play a lot of hide&seek but not a lot of play-fighting against one another like hunting animals do. Look at Dogs, they love to shake their toys for example which is essentially a training on how to shake small critters to death when they catch them. Chasing balls and other dogs is training for running and grabbing stuff etc. Cats on the other hand are smaller ans have more prey, they play a lot of hiding games with their owners and they can climb to safety or to catch food, and they love themselves a good tower of platforms to climb and feel safe in.
If your aquatics hunt fish then they will have games about learning how to fish, creativity building games which teach them the skills to create traps etc. Conversely if they eat only plants then they will have games about collection and memory etc.
The problem is that the exact games would be varied and there would still be some overlap. Hide&seek and tag are useful for both hunters and prey to perform to learn how to either hide, run or to sneak up to a target. So it would depend on exactly the amount of predators that hunt them, the way they specifically avoid each individual predator, the way they collect food, the way they hunt and collect etc.