Eden,
I understand there would be a few, but I do not have any information at hand on them. I had a very quick look at the www, without being able to locate a list of these words.
We are continually making up new words ("selfie", etc.) and the practice is not new. Even the word "atone" was an invented word:
http://hccl.byu.edu/classes/Rel212eh/Unit%202/15b-WordAtonement.pdf
At issue with theopneustos is that it is foolishness to build a theology on a new word that appears only once in the Scriptures, and that the context does not explain nor define. The later sparse use of the word applied it to non-Scripture, such as a tomb inscription.
The word is an adjective. It is not a verb. It does not describe an action taken by God. It describes the quality of the Hebrew writings that Timothy was exposed to when he was a child. The Bible did not exist when that verse was written.
The other matter of concern is the serious doubt that 2 Timothy was written by Paul, but was actually written by one of his adherents. Therefore, if a relevance could have been found in Paul's writings, it did not come from him.
Likewise with the only other reference raised in this matter - 2 Peter 1:20-21 - serious doubt has existed from the beginning of the Church Fathers that Peter wrote that epistle. Rather, it is dated to about 150 CE and was not written by one of Peter's adherents but by one of Paul's. (Jerusalem and Antioch were at loggerheads - a real tale of two cities). 2 Peter was written by someone familiar with Greek and with Greek thinking, not by an illiterate poor fisherman. Most agree that it is a commentary on the book of Jude and was hence produced much later.
So please accept my inability to help you find that list of "new and invented words". But if you do succeed, I would really love to knw.
Doug