That it was on a coin and whether Paul quoted it are an unproven connection that remains an opinion.
from That the World May Know:
The world of Asia was suddenly a very dangerous place for the rapidly growing Christian communities. The believers must be willing to call Caesar “Lord and God” or risk death. Everyone was expected to participate in the regular festivals in which he was acknowledged as divine. Before they entered a city they had to offer incense honoring him as god. This explains change from the book of Acts to Revelation. The emperors claimed not only the titles but the rights as well. They must be obeyed in whatever they demanded fop they were “gods” whether taxes, confiscation of property, or any other act. There was no escape for the believers. They could not buy in the market or conduct their business without acknowledging the authority of the emperor over the city. They could not walk through the city without stopping at his altars to acknowledge his “lordship.” They could not travel for every town they came to demanded their act of allegiance to the divine emperor. The public fountains providing drinking water for the towns and cities were devoted to the Emperor. Before drawing water one must acknowledge the emperor as the provider of life itself. And enforcing this Satanic policy? The incredible power of the greatest empire the world had ever known. No one had ever resisted its sword for very long. And the believers? Most were not the wealthy and powerful but ordinary people without influence on anyone. This was combined with the bloodthirsty character of the emperors themselves who did not hesitate to order people to suffer the most horrifying tortures ever devised. Nero, who used burning Christians as lights for his own banquets, who raped male and female Christians who had been arrested, who sent thousands to the arena to be torn to pieces in front of parents, children, and friends, set the standard for the treatment of these followers of the Galilean Rabbi. If you read the book of Revelation in light of these conditions, you are gripped by how virulently anti Roman it is, and what kind of suffering the believers were facing. But Caesar was not Lord! He just did not know it yet, even when the “atheist” Christians did.
So Jesus did not inspire Paul to write that...Well sure, I believe that...
If such a coin was found, it was copied from scripture...