One may compress a spring on a toy car so that the car will move forward, as long as the car does not make noise and no lights light up. One may not play with any battery-operated toy (17:2 above).
One may not blow up a balloon because a knot is usually tied at the end. However, if the balloon is sealed with a valve instead of a knot, and it has previously been inflated, it may be inflated on Shabbat (above 15:8).
Children may not play with toy musical instruments such as trumpets, pianos, guitars, bells, and noisemakers on Shabbat. Such toys are muktzeh. However, one may give a baby a toy that makes noise when it is shaken or a button is pushed. However, the adult himself may not cause the toy to make noise (MB 338:1; BHL s.v. “aval”; SSK 16:2-3 and n. 10; Harĥavot).
Sand is muktzeh unless it was set aside before Shabbat for children to play with (23:3 above). In that case, they may play with the sand as long as it is fine and dry enough that it cannot be used to fashion shapes. However, if the sand is wet enough that one can scoop out holes or fill them up, one may not play with it on account of the melakha of Boneh. One may not make sand wet, because of the melakha of Lash (15:2 above).
One may not play with marbles on the ground, because one may level the ground to make sure that the marbles roll smoothly. Similarly, one may not play any game on the ground that requires that the ground be flat, because one may end up leveling it. Even if the ground is paved, one may not play there, as there is a concern that one might then end up playing on unpaved ground. However, one may play on the floor inside; since all homes today have flooring, we are not worried that playing there will lead anyone to play outside on unpaved ground (15:2 above).
It is permissible to play with apricot pits, which children commonly play with; since they are set aside for this purpose by the children, they are not muktzeh like other pits. Even pits removed from apricots on Shabbat are not muktzeh, since many children play with them (see SSK ch. 16 n. 33).
One may swing on a swing, but if it hangs from a tree, even if only on one side, it is prohibited. If the swing hangs from a peg that was driven into the tree, it is permitted (19:7 above).