Sirius may also have tried every spell on the veil, like accio Harry and every spell that may be similar. Harry never tried to use the spell and it is possible that it would have worked on the veil. Sirius would definitely have tried to kill Bellatrix, but unlike Harry, he would have succeeded in his attempt. He would have tried to go in the veil after Harry, but may have been talked out of it by Remus who would tell him that Harry wouldn't want him to die for him. He would have been freed since he would have been seen crying over his godson. Sirius would most likely have been able to cope better since unlike when his brother and sister (in all that matters) were killed, he had his other friends, Harry's friends, and such. However, it is possible that Sirius would have lunged for Harry (since in the book, it wasn't the killing curse) and tried to pull him away from the veil before his godson was sucked inside.
It is possible that if Harry was closer than he was in the book, he would have ran in front of the spell, taking it for his godfather. In the movie, the spell hit Sirius' shoulder and it looked like if Sirius hadn't been standing there, the spell would have hit Harry instead.
story:
Bellatrix and Sirius were dueling. Sirius was laughing and dodging her spells. One particular red spell shot out unexpectadely. The spell was looming closer and was mere feet from Sirius' unprotected chest. Suddenly, there was a thump as if a body hit the stairs above. Sirius would check it out as soon as he woke up after getting stunned. Remus wouldn't allow him to stay unconscious near his sadistic cousin. However, those thoughts were gone as soon as a figure stopped in front of him and the figure was hit instead. Sirius was almost happy that he was spared . Almost, once he realized that the victim was his own godson, Harry. However, Harry was now falling into the veil, a mythical creation that was supposed to be the gateway between the living and the dead. However, not much was known about the veil. Sirius had no other thoughts than to get his godson away from the veil. He lunged and caught Harry's forearm. However, the arm was pulled out of his grasp by the pull of the veil on his godson. Sirius was in shock. He had lost his godson. In the corner of his eye, he could see Bellatrix running away, a sadistic gleam in her eye. Dumbledore was running after her, calling her names that Sirius didn't know he was capable of. He would have laughed if the situation wasn't more serious (no pun intended).
Sirius than got a plan. He ran to the veil. People have escaped from the veil before when they were conscious. Sirius ran to the veil, intent on jumping in and rescuing his godson. However, he was held back by Remus. Remus tried to reassure him that people were working on an attempt to save his favorite person in the world . Sirius pulled out his wand and mumbled a simple "accio Harry." However, after a few minutes, he gave up the hope that his godson would be saved by a simple spell. Then, a black robed man came into the room. Remus introduced him as the man in control of the chamber of death. The man was expert on this sort of thing. Sirius ran out of the room, intent on performing his new mission, kill Bellatrix Lestrange. Sirius found her laughing her manical laugh. He pulled out his wand, pointed it at her and prepared himself to mumble the spell that he refused to mumble since he joined the Order, the killing curse, Avada Kedavra. Bellatrix finally noticed him and sneered up at him. She then insulted, not just Sirius, but everyone that Sirius had ever cared about, except Pettigrew: Lily and James, Remus, Marlene, and then Harry himself, calling him a baby. Sirius snapped and performed the green colored spell. Bellatrix was now dead. He marched back to the chamber, to overhear Remus and the man talking about how it would be impossible to save Harry. The man agreed to try, but he didn't promise anything. Sirius made a small whimper, which the whole room heard, and fell to his knees and cried and made the worse sound anyone in the room had ever heard. Then, nearly the whole ministry entered the chamber. They saw the Death Eaters celebrating the death of Harry Potter. They also saw the Order, some of the DA, and Sirius Black, who the Order vouched was the one who had killed Bellatrix and was on their side. The man then exited the veil. He had a teenage boy with him with messy black hair, green eyes, and a scar on his forehead. It was unclear if the boy was dead or just unconscious. They rushed Harry St. Mungos hospital. However, Harry was dead on arrival. Sirius spent the rest of Harry's years at Hogwarts crying and getting comforted by his Order friends.