anvils, chains, rubber hosing, etc do make a
small amount of difference but to be honest it's nothing compared to having a lump without the bells on the end!
I have a small anvil in my outdoor workshop that I bought on ebay a few years back. The pics looked like it was a small london pattern anvil weighing about 40lbs. It turned out that it was a homemade anvil that was the shape of the classic anvil, but cut from 2 1/2" thick plate. That's not a problem really
It was very noisy to use, even when embedded and chained down under serious tension to a log buried in the ground. Then I chopped a couple of inches off the beak and that improved it a lot more than any of the "stick xxx on to it" methods.
My 50lb stump anvil set into a log is far far quieter than my 100kg london anvil that sits on a buried stump, with any attempt to dull the sounds. Most of those techniques that I tried ended up getting on my nerves in their own right anyway (magnets kept slipping off or I would catch things on them as I walked past, etc), heavy chains wrapped around it helped more than the magnet but got in the way sometimes, rubber stuck to it or wrapped around it obviously ended up getting me a face full of smoke
at the end of the day, make use of what you have. if trying to make a noisy anvl a bit quieter is easier/more cost efficient for you then do it.