I am still learning but here are a few suggestions that work for me:
Sign language and Basketball- I have found that senior primary really likes learning the sign language to the songs, I don't teach every word just the main ones. Then I have a group come up to do the sign language in front of everyone. If they do it well, they get to try to shoot a basket (paper ball into the trash). If they get it right they get some sort of priviledge (pick the next person to come up, put on a piece of a puzzle, whatever works for you). The thing the boys like is being able to throw a ball across the room!
You could do a similar idea with paper airplanes, or even kid darts if they allow that. You don't have to do it with sign language either. You could just say I am looking for good singers and especially be watching those kids who struggle the most, keep eye contact to show them you are watching them, and then as soon as they are doing it, pick them! Give multiple chances to throw in a day if that keeps them motivated. Walk around the room as they are singing and touch different kids if they are doing a good job, and they can reverently go to the front while continueing to sing (or have them wait until the song is over).
I also have teachers watch their classes and have them pick one or two kids who are singing well so I am not always the one watching.
