Adhesive carpet tiles. Cut to fit. You also can work with one at a time rather than wrestling with a large piece of carpet. Pick tiles with either no padding or something other than the foam on Cobra carpet, which disintegrates in a dry climate.
https://www.google.com/shopping/product/7442575094315953842?q=adhesive+carpet+tiles&prds=epd:18165453031383880840,eto:18165453031383880840_0,prmr:1&sa=X&ved=0ahUKEwjEjeH0-rPwAhUSM30KHQ_dDasQ9pwGCAY
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