I was a bit disappointed to read some of the replies and suggestions above. A number of stereotypes, in particular, were troubling.
For instance, that ten-year-olds are irresponsible, have short attention spans, lack commitment, and deserve cheap point and shoots from big box stores. They sure will be if you treat them like that. Instead of hypothesizing about the qualities of today's youth, might I suggest that the OP ascertain a few things before making any purchase: (1) what exactly did the kid like about the Leica experience (interchangeable lenses, viewfinder, focus, hi iso--don't laugh, you can check if he used hi iso and relied on it), (2) how big a camera is too big, (3) has the kid been careful with other possessions, (4) why is there no camera in the house?
The second stereotype is that a film camera from the 70s is the answer. Maybe some folk got their Leicas because their style is reminiscent of bygone eras of propriety and plenty when you could feed a whole family out of one dollar and there were twelve inches to the foot, or because they could never get over the 80s, 🙂, but a kid who enjoyed a digital back might feel very differently towards my Spotmatic than I do. Processing film can be time consuming and I believe the kid may want to be out there taking pictures. The OP can certainly show the kid how film is developed and see how he reacts, but because someone suffered with their EM and lawnmower decades ago doesn't mean that everyone must share the same, uh, character-building experience.
Third, mirrorless were quickly dismissed with shocked notions about focusing and modern gimmicks. Mirrorless need not be held at arms length, unless you are overly protective of your personal space. MFT has a bunch of electronic viewfinders. The Sony NEX has a flip up screen that works like a Rollei. Fuji has a hybrid viewfinder. The NEX is vastly superior in terms of the quality of its images to the M8 and will beat the M9 at high iso. It has a terrific peaking manual focus system that is fast, precise, and dependable in low light. I can manual focus an NEX faster than you a can a Leica and then make a movie of you catching up while you struggle with the focus shift of your f2.8 optimized Sonnar 50/1.5. MFT and the NEX also take Leica lenses for those times when the OP visits the kid and they need to praise together the performance of aspherical lenses wide open.
My last piece of advice is to really focus on which camera the kid would enjoy rather than the one you would. That will give you the answer regarding prime vs. zoom as well. I recommend a 50mm equivalent prime, but that may be because I started with a zoom and only later discovered the discipline building side effects of a prime. Taking the kid to Best Buy is a cheap way of getting out of the serious facilitator work you need to do and placing a fairly complex choice on someone with yet unarticulated preferences. A traditional camera store, that carries DSLRs, MFT and NEX, and even the Fuji x100, may be a better place for a ten year old to experiment with size, shooting style, and interchangeable lenses.