After the book Harry Potter and the Order of the Phoenix can Sirius Black still be alive?
This is not very likely. Sirius is most certainly truly dead. From Accio-Quote.org, a website of quotes from J.K. Rowling:
"Yeah. Well I had re-written the death, re-written it and that was it. It was definitive. And the person was definitely dead. And I walked into the kitchen crying and Neil said to me, 'What on earth is wrong?' and I said, 'Well, I've just killed the person.' Neil doesn't know who the person is. But I said, 'I've just killed the person.' And he said, 'Well, don't do it then.' I thought, 'a doctor' you know, and I said 'Well it just doesn't work like that. You are writing children's books, you need to be a ruthless killer.'"
See JKR quotes about death and the full interview.
However, it has been speculated that we may see Sirius again in '''Harry Potter and the Deathly Hallows''' either through the two-way mirror, by travelling back in time, or by Harry going through the veil.
in short yes he is dead however in his desperate attempt to find love he doses try to talk to Sirius through a tow way mirror. this will only have worked if he had taking the mirror with hem through the Vail. he did not do this so it was a total loss. i a short lived burst of hope harry thinks Sirius my have become a ghost. as for coming back in the 7 book that kinda happens exapt it is more like being a ghost. when harry gets the second hallow he brings back his mom, dad, lupin, Sirius. i have to reread it to See if he brings back tonks i think he doses.