Sirius did not give Harry the two-way mirror until Order of the Phoenix, almost 2 years after he escaped Azkaban and was reunited with Harry. Since then they spent much time finding difficult ways to communicate. Writing letters in code and through fireplaces which was extremely risky.
"Harry look back into the flames, and jumped. Sirius's head was sitting in the fire. If Harry hadn't seen Mr. Diggory do exactly this back in the Weasleys' kitchen, it would have scared him out of his wits. Instead, his face breaking into the first smile he had worn for days, he scrambled out of his chair, crouched down by the hearth, and said, "Sirius how are you doing?" Harry Potter Goblet of Fire page 331
Then later on page 332
He had let Harry talk himself into silence without interruption but now he said, "Dragons we can deal with, Harry, but we'll get to that in a minute-I haven't got long here... I've broken into a Wizarding house to use the fire, but they could be back at any time. There are things I need to warn you about."
It was also risky and dangerous to talk through the fire ask for example page 335
"Go!" he hissed at Sirius. "Go! There's someone coming!" Harry scramble to his feet, hiding the fire,- if someone saw Sirius's face within the walls of Hogwarts, they would raise an almighty uproar- the Ministry would get dragged in- he, Harry, would be questioned about Sirius's whereabouts-
Why didn't Sirius give Harry the two-way mirror he and James used to talk through when they were young. I know they hadn't seen each other since serious escaped on Buckbeak. He could have given it to Dumbledore to pass on to Harry. Why wait so long to give Harry a safe and easy way of communicating with each other?