What do you think of the name J.C.? It would be short for [name]James[/name] [name]Carson[/name].
I think [name]Jesus[/name] [name]Christ[/name].
I think JC Chasez or whatever from some 90s boy band. [name]James[/name] [name]Carson[/name] is a much more classy name than JC, unless there is a specific reason for shortening it, I prefer the full version, or something like [name]Jem[/name], [name]Jim[/name], or [name]Jimmy[/name].
I think it would be okay as a nn. Some might confuse it for the girls name [name]Jaycee[/name] I’ve been hearing more of lately. But as a nn for [name]James[/name] i think [name]Jim[/name] is cute for a little boy.
My mind first went to a “Famous in New Zealand” current affairs presenter, [name]John[/name] [name]Campbell[/name], who is colloquially called J.C. A few years ago there were badges (buttons) made with the slogan, “J.C for P.M” (P.M = Prime Minister). This is of course completely irrelevant to anyone outside of NZ! Oh well.
So, to give you a more useful answer to your question:
In general, I am not fond of initials as nicknames.
I think it could be problematic, do to the associations a few have mentioned ([name]Jesus[/name] [name]Christ[/name]; how it sounds like [name]Jacy[/name]). I have no problem with the [name]Jesus[/name] [name]Christ[/name] association, unless it’s done intentionally to be sacrilegious, but I know some people (mainly Jews) who are opposed to the [name]Jesus[/name] [name]Christ[/name] connection and all. I just wouldn’t want people thinking my son J. C. was [name]Jacy[/name], that would be my main concern. That, and I just don’t like initial nns. If my son had a gorgeous name like [name]James[/name], I don’t think I’d be able to stop calling him [name]James[/name]! J.C. (and really all initial nns) seem so lacklustre compared to the full and gorgeous [name]James[/name]. 
Good luck!
with JC I agree with others that I think of [name]Jesus[/name] [name]Christ[/name]. I’d suggest CJ but then I think of CJ [name]Craig[/name] form [name]West[/name] [name]Wing[/name]. I think that a nn like [name]Jamie[/name] would be better than the initials especially while still a child.
Not a fan of initials for nicknames. I know this is irrational, but the practice has always sounded like the parents couldn’t be bothered to call the poor child by his full name to me. [name]James[/name] [name]Carson[/name] gets full marks, though!
The name [name]Juan[/name] [name]Carlos[/name] is what I think of, which is often shortened to J.C. I also do not care for initials for names.
It makes me think of J.C. Chasez from Nsync. (<—I’m still a 90’s teenybopper at heart…lol) Personally, I have no problems with initial names. James Carson is very nice btw. Love James nn Jamey though.
As others have mentioned, I thought [name]Jesus[/name] [name]Christ[/name] first (I am not religious for what it’s worth, but grew up in a predominantly Christian community). Though I knew a J.C. in university, and didn’t think that when it was worn by a real person.
I think it’s harmless, if you like it. I personally like both [name]James[/name] and [name]Carson[/name] better than J.C. .
I think it’s a fine substitute to differentiate a somewhat common first name. My late great-uncle J.C. ([name]Joseph[/name] [name]Conor[/name],) was a jovial, loving gentleman, so the name does carry positive connotations for me, but also, even in our very Catholic family, no one ever associated J.C. with [name]Jesus[/name] [name]Christ[/name]. Really, I find it odd that people would nickname [name]Jesus[/name] at all.