If it's actual issue was with the tapes coming off, then what you really need to buy is a spare roll of diaper tape. I remember that they used to sell them at Babies R Us more than ten years ago when the adhesive tape in disposable baby diapers were not as strong as they are now (Hook & loop style as opposed to plain sticky tape back then). Unfortunately because the new baby diaper tapes are so effective, no one appears to sell spare rolls of diaper tape. I did find a manufacturer in China that exports to the US, rolls of diaper tape for adult and baby diapers but their client base are diaper manufacturers. They sell a single roll but the roll can consist of thousands of meters (1 meter ~ 3 feet) of tape (I don't think that you need nor can afford that much)! If you want to look just out of curiosity, here is the info:
https://www.alibaba.com/product-deta....28.0iVjbN&s=p
https://www.alibaba.com/showroom/adh...or-diaper.html
https://www.alibaba.com/product-deta...7.29.91.0iVjbN
I think that the best solution to your problem is to try using white 1" duct tape since it is the closest size (Height-wise) to the actual adult diaper tape. You could also try 2" duct tape for times when you're feeling a bit kinky (e.g. You could have mommy [Jen] wrap a length of 2" duct tape from one side [Left or right] of your diaper then across your diaper's waist band and continue on to the opposite side of the diaper for times when you're a naughty baby girl who has a nasty habit of tearing off her diaper and streaking like a Jay bird across the house! Bad baby! That should stop your nasty habit!) since you're into BDSM!
Here are some eBay listing for different kinds of duct tape that you might consider (All are low priced):
1" Colored Duct Tape (White would be best, IMHO)(Best value)
http://www.ebay.com/itm/Colored-Duct...RwLMjjDtzdcg0w
$10.74 for 1" x 180' (60 yards)
2" duct tape (White would be best, IMHO)
http://www.ebay.com/itm/1-54-Rolls-2...Fsp7ZTxUNp5yXQ
$4.39 for 2" x 60' (20 yards)
1.5" Barbie Design Pink duct tape (Cute novelty duct tape)
$3.82 for 1.55" x 30' (10 yards)
http://www.ebay.com/itm/NEW-Scotch-D...XmlbyWRkGR1JxQ
If you're not into duct tape, you can try using 2" diaper pins on your disposable diapers (You have to pin them on with a little slack and not tightly, otherwise they'll rip apart the sides of your disposable diaper):
2" diaper pins (Most economical and reusable)
http://www.ebay.com/itm/10-50-Pcs-Pl...iIu58Hg2iKo2ig
10 for $0.99.
I hope that this all helps.

