Im sorry to hear about your cousin, my feelings go out to you.
But as it so happens Im a bit of a writter myself thats also taking a child development class. While i dont have any ideas upfront, i can give you a few tips to get started:
1: The age group.
18 months - toddlers tend to have a somewhat short attention span and need a simple, straight forward story that keep their attention. 1st graders and up you can start adding a little depth to your stories.
2: The occation
Certin stories are more appropiate then others. Is it just a story before bed? Are you trying to teach them something? Cultural awarness? A holiday story? This is also something you need to think about.
Those are the only two real tips i can give you. But as a few extra suggesions, children love animals thats a no-brainer), especialy talking ones. Ryming is also a great tool to use. Its fun and tends to keep their attention.
Now by no means am i profesional writer or a expert on children. These are just a few things ive picked up here and there from working with them. And please forgive and misspellings as i typing this on my iPod and this tiny keyboard is a pain in the a**.