The best we can hope to do here is summarize exactly who did what and explain why the debate exists.
That's it. That's the best we can do. So I'm going to start gathering evidence for the various claimants. There's no way I can finish it tonight, but I'll start.
Gould sketched an idea for a laser in 1957 and then had his idea notarized (at a candy store, apparently). He coined the term laser in the notes beside it. He didn't build anything until 1958, and so only filed for a patent in 1959, at which point others had already patented the idea. He did announce his idea at a conference that year, but it didn't help him secure the patent.
Maiman built the first operational laser in 1960 at Hughes Research Laboratories. His design was tiny and used ruby, but it was successful, and HRL claimed that he was the laser's inventor.
Charles Townes and Arthur Schawlow
The duo had already patented their maser design in 1954. In 1958, they came up with theoretical models of a derivative of the idea using visible light, but did no further research. They are able to patent their design in 1960.
There's not a non-opinion-based definitive answer here.
National Laser Company and photonics.com