I second the wait until your parents are out for the day and schedule it for then, worst case they see the box, it's ok the first, maybe second time but if you revive the same box each month or so, they will start to get supscious. You can use this method if you are absolutely desprete (saying you are stuck in isolation or something) I personally use this if I'm in isolation and I need more nappies (I use for my OAB, so I will need more each week) my parents wouldn't notice me ordering for nappies if I only order and have it delivered to the house every now and again, unless I did it excessively and then they would worry that I was hoarding or something. One thing about the diapers I order are the Tena ones and they come in a small package so they won't wonder what I ordered each time it comes to the house,
Another option which I use (I'm 22 and I still live with parents), is that I go on eBay and order my diapers, when I go onto the checkout section, I click on "click and collect" and choose my location and then pay like normal, after that you will get a email saying that you placed the order and that you can't pick up the order without a barcode (you will get an email when it's ready to be picked up with a barcode that the cashier will scan before getting your parcel) I use a carrier bag and carry the box home and just go upstairs (it's really not noticable unless you order a big order!) this is my go to method getting my nappies whilst living with my parents and I almost use it every week. This way you are guaranteed not to get caught since nobody knows what's in the package but you and your parents are not answering the door.
By the way, EBay does sell ABDL diapers, pacifiers and clothes, you just need to look and more often than not, with a bit of scrolling you can find cheaper diapers! If you want to get some toys as well, I use the same method, but I'm more likely to get them delivered to the house.