I guess my idea of what constitutes a "babyish" diaper has been influenced by the ones I would have worn growing up, compounded with the types of diapers I saw the babies in my family using when I was a teenager. I therefore tend to imagine an all-white plastic or cloth-backed disposable with some sort of front panel design, so SDKs, Bellissimos, Carousels, PeekABUs, Preschools, and maybe Teddys all fit the bill.
With more and more real baby diapers now using all-over prints, I suppose it's increasingly hard to argue that designs like the ABU Kiddo aren't "babyish" by 2018 standards - but they are babyish only in that they tend to emulate baby diapers from a later time period than what I tend to use as a reference point. TBH, I suppose if I grew up surrounded by children wearing primarily cloth diapers and plastic pants, that would be the epitome of "babyish" to me now.