Don’t play with dead balls.
The same argument that applies to rackets applies equally, in fact more so, to tennis balls. It is not possible to hit old, light, worn-out tennis balls of any degree of accuracy. Play with new balls. The fuzz on the covering of a new ball keeps it in true flight in the same way that feathers keep an arrow in true flight. Pressure in a new ball will deliver the correct and consistent bounce.
Children that are learning to play the game especially in the three four and five-year-old bracket might want to start with the new beginner tennis balls: Kids balls: Prince Play & Stay Stage 1 Tennis Ball Can