Several different schema for developmental stages have been used by different psychologists. Step One for this assignment is to choose one, which your textbook may help you do.
The next step will be specifying the elements of your stage for which you will perform your design. This is where good keywords come from!
For example, Piaget's cognitive development stages include a "concrete operational" stage. There will be articles that discuss this stage directly, but you're much more likely to find results that talk about specific *elements* of the stage. These also make for easier design work. Look for ideas such as:
There are a few call number ranges that may be of special significance when you're looking for resources about how to design.
BF717 - Play in child development
HQ767.9 (and similar) - Child social development
LB1029 (and similar) - Educational toys and games
RJ504 (and similar) - Child psychiatry including play therapy