In old times the word "gay" meant only "cheerful","sprightly","vivacious","blithe" , "bright" ...
In those years for many peoples "Gay" was a nice first name.
Now "Gay" is for omosexual person.
Was possible an alternate term for "omosexual" different from "gay"?
(please,none vulgarity.
Thanks).
Sorry for the nitpick, but it's homosexual, not omosexual.
Omo- refers to the shoulder, so omosexual would be an odd construction indeed. (Noted because the usage of that twice indicated pattern and your posting suggests a non-native English to the ESL teacher. Hope you don't mind the correction.

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As to the word gay, it has a pretty established history of "immoral" meaning.
The suggestion of immorality in the word can be traced back to 1637.
http://www.etymonline.com/index.php?term=gay
But, maybe glad would do? It's similar in sound and has some entertaining double entendre possibilities, such as glad hand and glad rags.
Actually, the sky is the limit here. Given the number of new words that were coined in the fifties and sixties (beatnik, hippie, groovy and more) it is surprising they would choose to re-define an established word.
Gay was already well in use by the fifties and sixties, but yeah, otherwise, spot on.
Rawson ["Wicked Words"] notes a male prostitute using gay in reference to male homosexuals (but also to female prostitutes) in London's notorious Cleveland Street Scandal of 1889. Ayto ["20th Century Words"] calls attention to the ambiguous use of the word in the 1868 song "The Gay Young Clerk in the Dry Goods Store," by U.S. female impersonator Will S. Hays.
http://www.etymonline.com/index.php?term=gay
I've always liked my own theory that 'gay fella' is a variant of 'faygella' (the latter being a Yiddish term for the same thing). I seem to remember that my theory was shot down in flames by reference to facts, b/u/t/ I/ d/o/n't/ c/a/r/e/, it's a fun theory.
translate the Yiddish: Birdy?
Interestingly, the Online Etymology Dictionary suggests that it "may also be reinforced by Yiddish faygele 'homosexual,' lit. 'little bird.'"
http://www.etymonline.com/index.php?search=fag
Do note that's reinforced by, not derived from.