Romans 13.10 ἡ ἀγάπη τῷ πλησίον κακὸν οὐκ ἐργάζεται πλήρωμα οὖν νόμου ἡ ἀγάπη
Colossians 3.14 14ἐπὶ πᾶσιν δὲ τούτοις τὴν ἀγάπην ὅ ἐστιν σύνδεσμος τῆς τελειότητος
Ephesians 2.8 Τῇ γὰρ χάριτί ἐστε σεσῳσμένοι διὰ πίστεως καὶ τοῦτο οὐκ ἐξ ὑμῶν θεοῦ τὸ δῶρον
So, the verses in Romans and Colossians should both use love as a base translation. However, one could argue that this is a benevolent love. In addition, the KJV was written using English that is now 400 years old. So, the use of charity is a bit loose but not unreasonable.
In addition, your statement that the translators used only Greek texts is most likely incorrect. Quite possibly, the committee conducted their work while speaking Latin, and they likely relied on Latin texts as well.
I included Ephesians 2.8 as well, as this demonstrates the problem with translating agape as charity. The Greek word we typically translate as grace is χάριτί, or "charity." Intermingling the two Greek words muddies the waters for those doing in-depth study.
This is the problem with fixating on very old works, apart from a purely academic perspective. Scholarship has produced a vastly more precise Greek text and a much deeper understanding of the Koine Greek of that text.
I want to clarify my phrase
is χάριτί, or "charity."
I meant the quoted word to be a transliteration of the Greek word, not a translation.
From the comments, I looked at the origin of the English word, charity. I assumed it came from the Greek, but that is not correct. It comes from Latin, and the Latin word can be mean love, in a benevolent sense. That helps me to understand why the Vulgate uses the Latin word, and why the KJV followed the Vulgate.
The Cambridge English Dictionary has a secondary definition of charity.
the quality of being kind to people and not judging them in a severe way
This is what I meant by an out of date definition; I don't hear that word used that way much anymore.