Origin of "off-color"
Solution 1:
The earliest use, according to the OED, seems to have been in 1860 in the diamond industry, where it described a diamond that was ‘neither pure white nor any definite colour, and so of inferior value.’
Thirteen years later it was used to mean ‘Not of a colour considered natural, proper, or acceptable; paler or darker than expected or usual.’ Three years after that was in extended use to mean ‘Not in good health, slightly unwell; (also) not up to the mark, defective, deficient, out of order.’
Around the same time it was also in use to describe something that was ‘Of questionable taste, disreputable; improper, vulgar; specifically (of language, jokes, etc.) slightly indecent or obscene.’