Personally, I ordered from Nappies R Us. I think that they're in some way affiliated with abdlmarketplace, as when I was sent an email saying an item was out of stock, I ordered a different item that was only stocked in the other website, and it came fine.
Also they're really good with discrete packaging: My order arrived in grey plastic packaging; unmarked (other than for address), but it wasn't a box, so if you were suspicious, you could definitely tell they were diapers from the feel of the package.
The other reason for which I'd recommend them, is that as this was my first ever order of abdl supplies, I was really paranoid about being found out, so I was really grateful when I discovered that even the transaction ID on my bank statement said something that wouldn't give it away (like Paypal:GDHL or something). They do pretty good prices too.