JoAnn Fabrics has two grades that are 60" wide and sold by the yard. The craft felt is the least expensive and is on sale from time to time. It is polyester.
The good stuff is thicker, has some natural fibers in it and is 2x the cost.
I use 3M 77 Spray adhesive around the edges and fit the felt with a little tension and trim the edges with a utility knife or box cutter with a fresh blade when dry.
The outdoor carpet will have a rubber backing for some sound absorption. Tough to find the right color in a tight weave, but you can. You can spray glue that down, too. About the same in cost as the good felt.