"Any ways various groups could try to be politically correct about the children?"
"So what nicknames could the kid's as a group have?"
Well, in my experience with real minorities, generally there are three categories of terms. Within each category, there's typically at least two terms, if not more.
Insults relating to that group - with these kids, you might use things like 'mutant', 'freak', 'devil child' (if there's sizeable religious prejudice against them), 'walking nuke'
Politically correct terms - 'people with special powers', 'children born from the coma epidemic', etc.
Terms the people themselves use - typically, the politically correct types see no difference between these and the offensive terms, and occasionally the same word is in either category depending on who's using it and how (a real life example would be the word 'gay'). These kids might use 'blackout babies', 'supes', 'psychics', 'generation psi', etc.
If I'm asking for advice on a story idea, don't tell me it can't be done.