There is the Spotlight Live restaurant in the middle of Times Square. Very good sound stage but they do lack in song selection. Food/drink prices are high too and you have to pay $5 for a wristband before you can get to sing.
Not my personal choice for a venue, but your singers may be interested. They also are running a contest with the overall winner getting a recording contract with Epic records.
Their website is
www.spotlightlive.com
One of the favourites of mine for NYC is saxappealmusic. I don't think they have a venue in the city on the weekends any more, but I know they used to be at Gael's Pub on Sunday nights. They do have gigs on Tues, Wed and Thursday a few blocks from Penn Station. Check out their calendar at
www.saxappealmusic.com
In Little Italy there is the Mulberry St Bar, Mulberry Street Bar (at 176 1/2 Mulberry St). I think they have karaoke Thurs, Fri and Sat nights, maybe Sunday too.
Coogan's has karaoke Tuedays Thursdays and Saturdays. Never been there myself so can't give an opinion.
www.coogans.com/sections/kar.htm
Another posibility is Mr Biggs, 596 10th Ave (between 43rd St & 44th St)