They tried calling the gorillas away from the enclosure which would have allowed them to get the kid out without hurting any of them. The others obeyed, the male who was shot didn't. I don't see they had other options without endangering human lives.
Agreed, anything else they tried to do could've resulted in the gorilla becoming mad and harming the child. Tranq the gorilla, he's not going to pass out immediately (yahoo answers says 10 minutes is the norm), but he has a sharp needle in his ass which is surely gonna piss him off. As davedan said, the barbituates would also make him drowzy and confused, and like humans, the gorilla wouldn't be in his right state of mind, which could make the situation worse. Sending a bigger adult to get the child may make the gorilla territorial and at the very least puts another person in danger. Trying a nonlethal shot has the same effect as the tranq, but without knocking the gorilla out in 10 minutes. The only other option is to do what the zoo did, call the gorillas away from the child to make it safe for someone to go in and save him. The other gorillas complied, Harambe did not, and that forced the difficult decision.
It is a tragedy that the gorilla had to go, but the zoo made the right choice to save the child. I really want to see some kind of criminal punishment for the mother (like really, how does your 4 year old fall into a gorilla enclosure). But, nevertheless, the zoo did the right thing.