Oh... that kind of carpet.
You might look at an auto upholstery supply store/website for foam backed headliner and foam backed carpeting. J&J Auto Fabrics in Rialto, CA is a good source and they will send out samples on request. These are really good peeps and if they don't have what you want, they will usually help find a source.
Their website is www.jjautofabrics.com
You can also check out marine supply sources for what they call "Hull Liner", but expect to pay more than you ever imagined.....