Courteous (krt-s; 277), a.
Etymology: [OE. cortais, corteis, cortois, rarely corteous, OF. corties, corteis, F. courtois. See Court.]
Of courtlike manners; pertaining to, or exxpressive of, courtesy; characterized by courtesy; civil; obliging; well bred; polite; affable; complaisant. A patient and courteous bearing. Prescott. His behavior toward his people is grave and courteous. Fuller.
Shades of meaning
Fernald has no entry of its own for courteous; he lists it under polite.
Where he writes about it:
Civil is a colder and more distant word than polite; courteous is fuller and richer, dealing often with greater matters, and is used only in the good sense. — from polite
Genteel refers to an external elegance, which may be showy and superficial, and the word is thus inferior to polite or courteous. — from polite