If your bike has a derailleur mount, XLC makes single wheel chain tensioners that will take the slack out and probably quiet the drive system down at the same time. They are common on BMX bikes.

Here's the one I recently ordered for my 5spd IGH chain drive beach cruiser:

XLC Single Speed Chain Tensioner Singleator style | eBay

There are much more expensive models out there like the Surly Singeator.