As an italian who is familiar with soccer fans (but consider that in my country, we've many many problems with them) I've some idea.
1) The community can prepare/imagine some songs/chants/chorus to sing during the games. Maybe 3-4-5 songs with rhymes, that are pretty good. Of course these songs are good to cheer the team and the single players.
2) The organization, with the fans, can organize some choreographies, to show before the puck drop. These ones can be useful to bring more color into the building.
Of course, you've to know that in Italy, these fans who want to sing during the match, are in a specific sector of the building. In NHL I think that in every part of the Amalie Arena, there're people with kids or, simply, people who want to see the game quietly. And of course you cannot say: "Go away".
I've to say another thing, to be honest. I'm familiar with the Italian fans, but I've seen one hockey match in Canada (Lightning @ Maple Leafs, in October 2016, 7-3 win for us). And I've loved the atmosphere in the Air Canada Center. I like the "American cheer style", to be honest. And I think it's better than the Italian one, with his problems. As Gianluigi Buffon (the former Juventus of Turin goalie) said: "The fans cannot score a goal". So, imho, the building, apparently quiet, is not a big problem.