Can I use these words?
A gay couple (not sure if couple can be used only for married people)
A gay lovers (not sure if I should put s here or if lovers can be used to describe two people who love each other)
You can say they are a gay couple or they are gay lovers to refer to two gays in love with each other and not necessarily married.
Assuming they're not legally married, gay and Lesbian couples usually refer to each other as "my partner" when speaking to others. If they are married, variations on husband and wife are used. Sometimes a gay relationship will have two husbands, two wives, or a husband and a wife.
If the relationship is less formal, boyfriend and girlfriend are often used.
I have no citation for this; it's just what I've heard and observed.
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