This is a question that has been going around on the internet, and I'm not sure if J.K. Rowling has answered it. If someone could find a quote or interview or tweet etc. of J.K. Rowling replying to this question, that would be great.
Sirius liked women
The teenage Sirius had plastered the walls with so many posters and pictures that little of the walls’ silvery-gray silk was visible. Harry could only assume that Sirius’s parents had been unable to remove the Permanent Sticking Charm that kept them on the wall, because he was sure they would not have appreciated their eldest son’s taste in decoration. Sirius seemed to have gone out of his way to annoy his parents. There were several large Gryffindor banners, faded scarlet and gold, just to underline his difference from all the rest of the Slytherin family. There were many pictures of Muggle motorcycles, and also (Harry had to admire Sirius’s nerve) several posters of bikini-clad Muggle girls; Harry could tell that they were Muggles because they remained quite stationary within their pictures, faded smiles and glazed eyes frozen on the paper. This was in contrast to the only Wizarding photograph on the walls, which was a picture of four Hogwarts students standing arm in arm, laughing at the camera.
Harry Potter and the Deathly Hallows - Chapter 10
Women liked Sirius
It had never occurred to Remus that Tonks could return his feelings because he had become so used to considering himself unclean and unworthy. One night when they lay in hiding outside a known Death Eater’s house, after a year of increasingly warm friendship, Tonks made an idle remark about one of their fellow Order members (‘He’s still handsome, isn’t he, even after Azkaban?’). Before he could stop himself, Remus had replied bitterly that he supposed she had fallen for his old friend (‘He always got the women.’). At this, Tonks became suddenly angry. ‘You’d know perfectly well who I’ve fallen for, if you weren’t too busy feeling sorry for yourself to notice.’
Note that Rowling considers having previous relationships with women to be an indicator that a character is not gay.
Recently I was in a script read through for the sixth film, and they had Dumbledore saying a line to Harry early in the script saying I knew a girl once, whose hair… [laughter]. I had to write a little note in the margin and slide it along to the scriptwriter, “Dumbledore’s gay!”
J. K. Rowling at Carnegie Hall, 19 October 2007
Since I posted this answer the question has been edited to specifically ask whether JK Rowling ever answered the question.
In September of 2016, Rowling updated her twitter bio to say:
FAQ answers: 1) Because the Basilisk didn't kill him 2) Next year, I hope 3) Yes 4) Wait and see 5) No, he isn't 6) No, he really isn't 7) Yes, I'm sure."
This for some inexplicable reason led a lot of people to assume that Rowling was saying that Sirius wasn't gay.
hoImesnwatson: are questions 5, 6 and 7 about sirius???? i'm confused pls answer
J.K. Rowling: No, the last three 'answers' in my bio refer to the person who has dominated my notifications for the past 5 days.
I would have thought it was kind of obvious if you look back over my timeline.
Thanks for the polite question, though!
To the best of my knowledge this is the only time that Rowling directly responded to someone asking a question about Sirius's sexuality. And Rowling has previously said that she would never hold back information on characters being gay if directly asked.
Razia Iqbal: You've just come back from a tour in the States where you made the news in all kinds of ways, not least because you revealed that Dumbledore is gay. Had you always seen him as gay in your mind?
J.K. Rowling: Yeah. Always. No one ever asked me. No one ever asked me "Has he ever been in love?" or "Who did he love?" No. People have been very focused on what happens to Harry. So I've never been asked a direct question. And because I have never been asked a direct question, and also because to answer it would immediately flag up an infatuation that happens in Book Seven, I've never said it. If I've been asked, though, I would have said it, of course.
Iqbal, Razia. Videotaped interview of J.K. Rowling, BBC News, 1 November 2007.
JKR never stated either way (but she said he had no girlfriend).
J.K. Rowling does say that Sirius never married because he was “too busy being a rebel”.
Does Harry have a godmother? If so, will she make an appearance in future books?
No, he doesn’t. I have thought this through. If Sirius had married… Sirius was too busy being a big rebel to get married. When Harry was born, it was at the very height of Voldemort fever last time so his christening was a very hurried, quiet affair with just Sirius, just the best friend. At that point it looked as if the Potters would have to go into hiding so obviously they could not do the big christening thing and invite lots of people. Sirius is the only one, unfortunately. I have got to be careful what I say there, haven’t I?
Edinburgh Book Festival interview (August 15, 2004)
She further mentions in a different interview when asked the same question that he didn’t have a girlfriend, either.
ES: Who is Harry's godmother?
JKR: Didn't have one.
JKR: Well, Sirius never had time to get a girlfriend, let alone marry.
- Leaky Cauldron interview (July 16, 2005)
However, she doesn’t say anything about Sirius’s preferences either way.
There isn’t any canon evidence that he is...
There’s nothing in either the books or movies that shows Sirius Black as having either a relationship or attraction to a guy, nor is there an after-the-fact declaration that he was gay. There are a few quotes that some fans interpret in a way that implies that Sirius was in love with Remus Lupin such as them “embracing like brothers”, but there’s nothing that’s anywhere near close to stating that he was.
...but there’s only slight canon evidence that he isn’t.
Sirius Black is never mentioned as having a serious relationship with anyone, whether male or female. The only thing indicating he might be interested in women is that he had pictures of Muggle women in bikinis on his wall, but that doesn’t necessarily mean that he was attracted to women.
“Harry could only assume that Sirius’s parents had been unable to remove the Permanent Sticking Charm that kept them on the wall, because he was sure they would not have appreciated their eldest son’s taste in decoration. Sirius seemed to have gone out of his way to annoy his parents. There were several large Gryffindor banners, faded scarlet and gold, just to underline his difference from all the rest of the Slytherin family. There were many pictures of Muggle motorcycles, and also (Harry had to admire Sirius’s nerve) several posters of bikini-clad Muggle girls; Harry could tell that they were Muggles because they remained quite stationary within their pictures, faded smiles and glazed eyes frozen on the paper.”
- Harry Potter and the Deathly Hallows, Chapter 10 (Kreacher’s Tale)
It seems like most of Sirius’s decorating style is designed to annoy his parents - which also means he’d expect they’d see it. With their strict desire to keep the Black bloodline pure, Sirius’s parents would be likely more upset with him being interested in Muggle women than Muggle men - with a Muggle woman he could reproduce and taint the bloodline. If he’s simply trying to anger his parents, that might get a bigger reaction.
He was also shown to be somewhat popular with girls, but there doesn’t seem to be any evidence in the books that he was pursuing them back.
“Sirius was lounging in his chair at his ease, tilting it back on two legs. He was very good-looking; his dark hair fell into his eyes with a sort of casual elegance neither James’s nor Harry’s could ever have achieved, and a girl sitting behind him was eyeing him hopefully, though he didn’t seem to have noticed.”
- Harry Potter and the Order of the Phoenix, Chapter 28 (Snape’s Worst Memory)
In fact, I couldn’t find any evidence of him actually showing interest in a girl. James is shown taking an interest in the girls who followed him around Hogwarts, but Sirius never was shown as interested - he was haughty and aloof.