It depends on what you mean by "depicting a homosexual couple".

The Alfred Hitchcock movie 'Rope' was made in 1948. It was based on a play of the same name, written in 1929, which was in turn based on the real-life story of a pair of gay men in their 20s who murdered a teenager just for kicks: Leopold and Loeb. Obviously, the play and the movie didn't use the real names and were dramatised.

While the pair of killers weren't actually presented as gay in the movie, they were still two young men who lived together and who showed slight signs of homosexuality (as much as the director could get past the censor!). It was, of course, common knowledge that the movie was based on the play, which was based on Leopold and Loeb. Some cinemas refused to show the movie because of the subject matter. The review by Time magazine openly mentions the "lavender dandyism" depicted in the film, which is code for "homosexual".

However, at no time in the film is it stated or shown that the two killers are gay. There's no affection between the two, no kissing, no touching, no mention of love or a relationship. On the surface, they are merely two young men who live together. But everyone knew the truth.

'The Killing of Sister George', made in 1968 (based on the 1964 play of the same name) had another subtextual homosexual couple: a pair of women who live together in an abusive relationship. Like 'Rope', it is never stated that the two women are homosexual, but it's hinted very strongly.

The first openly gay couple in a movie were Hank and Larry in 'The Boys in the Band', made in 1970 (another movie based on a play). Not only was there a gay couple, but most of the characters were gay. The characters were friends, gathered in one man's apartment to celebrate his birthday. According to The New York Times, "the celebrants include what is apparently meant to be a cross-section of homosexual types". This was a cutting-edge movie, openly depicting gay men on the screen, warts and all, for the first time.

In his autobiography, the director William Friedkin says that he went out of his way to film an extra scene (only mentioned in the play) which showed Hank and Larry kissing. However, he cut this scene during editing as he felt it was too sensational.