German, for whatever weird reason, thinks anything is cuter, nicer, hinreißender if its gender has been removed. (Let's not get all Freudian about this, okay? Keep in mind that the words have gender, not the objects they represent.
If you're going to get cutesy on something in German, you do that by adding a suffix and an umlaut where possible (or not, just to be trotzig, particularly in southern dialects), and, um, neutering it.
Exactly which suffix you'll use might depend on the region.
|das Päckchen, Packerl
|das Küchlein, Küchle
|das Weib 1
|das Fräulein 1
|*die Mad 2
|die Katze, der Kater
|das Stückchen, Stückerl
So what about the word for "boy"? One might rightfully expect a diminutive das word for boy, following the same pattern. There is one, but it doesn't seem contemporary: Bübchen. If there is a more commonly-used neuter, diminutive word for male children, please let us know about it in the comments.
Getting the gender wrong on stuff is frustrating, but it happens, and it's pretty much never fatal. But on diminutives, you don't have to. The rule is very reliable: Neuter is cuter.
- My host father used it against his ten-year-old daughter who was having a diabetic freak-out in the early 1990s.
- A senior citizen couple used it to attract the attention of the young waitress last year in a Biergarten, and they obviously meant nothing negative by it.
- We are not aware of a commonly-used non-diminiutive word for bunny, other than Hase (and that's arguably not the word for bunny). German Wikipedia reports Kanin as an archaic term still in use among furriers. There are more terms, like Kanickel, Karnickel, Künglein, and Chinigl, but they all appear to have a diminutive tacked onto them and may also be obsolete anyway.
- Apart from Watership Down and Donnie Darko, show me any bunny who is not worthy of a cutifier.