I have actually seen quite A lot of civets in zoos.
Banded palm (Cincinnati, Columbus)
Small Indian-(Dusit zoo)
Asian palm-(Khao Yai national park)
Masked palm-(Shanghai zoo)
Banded linsang-(night safari Singapore)
Owston's palm-(Newquay zoo)
Small toothed palm -(Bronx)
African civet- (Axe valley Bird and Animal park)
It was a while ago so I don't remember the day at all but I do remember the linsang. I believe the safari staff obtained from the wild and used it as an animal ambassador. I think the zookeeper who had it was showing it around to some guests. I am not sure they have it anymore but I took some pictures so I think I might be able to show you. But I cannot guarantee anything.
Ok so it turns out that the Singapore Night safari had it as a animal ambassador and switched with a few other asian zoological parks. (I believe Taman safari?)
I honestly have no idea if they are at Taman safari now, Since I was there about 7 years ago.
But like I said, I believe they were animal ambassadors so many of the people that visited might have not seen it.