Here's a new signup form where we can request free Cuties diapers. Scroll down to find the signup form and you'll get both a freebie and a $5 off coupon.
There's also this older signup form that I think is still active. Enter your email, then you'll immediately receive a message with a link to the signup address form. Samples will ship within 3-5 business days!
If either of these forms go down, just tell your kid to hold it for a while. I'm sure they'll understand.