Word Usage – Make or Say with ‘Prayer’ Explained

This sense of can is what linguists call a negative polarity item (NPI). You're already aware that can't can be used to mean "is not possible", and you clearly have little difficulty accepting that can can be used to mean "is possible" when the context effectively negates it ("I don't think that …"). So the tricky part is just recognizing that in English, negative polarity items are also licensed by (i.e., allowed to occur in the context of) questions.

Another negative polarity item is any; as you can see from these examples, they have similar distributions:

• Direct negation:
  • 1 isn't greater than any other positive integers.
  • 2 can't be greater than 3.
• Negation in a matrix (containing) clause:
  • I don't think 1 is greater than any other positive integers.
  • I don't think that 2 can be greater than 3.
• A question:
  • Is 1 greater than any other positive integers?
  • Can 2 be greater than 3?
• Use after only:
  • Only 1 is greater than any other positive integers. [This is false, of course, but the statement is grammatical.]
  • Only 2 can be greater than 3. [Ditto.]

Note that not all NPIs are licensed by the exact same contexts: some require more thoroughly negative contexts than others. Also, a word can be an NPI in one dialect, or in one register, without being an NPI in a different dialect or register. So this is a rough observation, rather than an firm guarantee of identical behavior. But it's a good first approximation.

My gut feeling aligns with yours – it sounds off to me. I did some research on Google that seems to confirm our hunches.

One reason it sounds off, I think, is because kid and boy both connote a young age. So, the phrase sounds redundant. You could simply say:

There was a boy hurling stones at a cute puppy.

or:

There was a kid hurling stones at a cute puppy.

I suppose one could argue that a "boy" could be an adoloscent, so, some clarification about age might be in order. However, if you wanted to clarify, you could say:

There was a young boy hurling stones at a cute puppy.

Ngrams found plenty of hits for "a young boy" and "a young girl," but came back empty-handed for "a kid boy" and "a kid girl".

I found several hits on Google for "a kid boy", but they were excellent examples of why hit counts need to be examined carefully. Many of them had extra punctuation, like this:

If you had a kid, boy or girl, and wanted to know...

Some even used the word boy as an exclamation, like this Pinterest tag:

Pins about: Toys I had as a kid. Boy I miss them!

There were several hits that were labels to stock illustrations:

Illustration of a Kid Boy Dressed as Prince Sitting on a Student Chair

but redundancy makes sense in that context, because those who title images in an image database want customers to get hits if they search for boy or search for kid.

But I'd avoid it in a context like the one you are asking about.