I tried communicationally, but the Free Dictionary doesn’t find it to be a word.
What I am trying to express is that someone is communicationally challenged, basically meaning they can’t communicate very well.
Just because a term does not appear in this or that dictionary does not make it “not a word”. For one thing, the “Free Dictionary” falls short of being an accepted standard in the English language.
But for another, productive affixes like un- and -ly can be applied to virtually any word from the target class to produce a perfectly viable new word. So even if you were using a little dictionary that happened to be missing an headword for something like unceremoniously, no one would ever question it if you used it.
So with your particular case of
you certainly you could do so. However, whether you should be creating such septasyllabic monsters is something else again; you might well want to use a longer phrase here instead.
You could just say they don’t communicate well, or that they’re poor communicators. All those, and many others, seem an improvement over the ponderous communicationally challenged.
The Wiktionary has an entry for communicationally.
But if you want another word, incommunicable means "who does not communicate freely".
The post was tagged "adverbs", but "communicationally challenged" as a whole is an adjective, and "incommunicable" is an adjective.
There is an entry for communicationally in the Oxford English Dictionary with the definition 'as regards communication; in respect of communications.'
The most recent citation for communicationally
…in my copy of the OED is in the context of communicationally challenged:
This is probably no coincidence, since it is a snug fit with the snowclone pattern:
Depending on the context, though, you may also have the choice of using the word communicatively:
Notice that there is quite a bit of overlap in the definitions of the two words, and this form is 16 times more common than communicationally in the COCA. Ngrams shows a similar disparity: