In the beginning I used to but later decided that diapers are even more comfortable after some wetting. They're fluffy wrappers for your derriere and either way they're nice to wear.
At least in the Canadian case it was a rather large box (probably around 1/2 the size of a door frame) but otherwise plain and unremarkable. I don't remember any visible signs that it was a package of diapers.
I only began indulging in diapers when I moved into an apartment so it should be 100% secret. My family knows I'm keeping something secret here but they would never imagine it's a stash of diapers!