The applicable statute (Section 23-31-235) states:
"(B) All signs must be posted at each entrance into a building where a concealable weapon permit holder is prohibited from carrying a concealable weapon and must be:
(1) clearly visible from outside the building;
(2) eight inches wide by twelve inches tall in size;
(3) contain the words “NO CONCEALABLE WEAPONS ALLOWED” in black one inch tall uppercase type at the bottom of the sign and centered between the lateral edges of the sign;
(4) contain a black silhouette of a handgun inside a circle seven inches in diameter with a diagonal line that runs from the lower left to the upper right at a forty five degree angle from the horizontal;
(5) a diameter of a circle; and
(6) placed not less than forty inches and not more than sixty inches from the bottom of the building’s entrance door."
The sign posting you have described may or may not be in complete compliance with the law, depending on the distance of the sign from the bottom of the adjacent door. The law does not appear to require that the sign be on the door itself. "Clearly visble from outside the building" is subjective, but your description seems to qualify. Personally, I wouldn't take the chance that a judge or jury is going to take your side if positioning of the sign misses the requirements by a few inches.