There are flame proof rugs . I used oil change pan on my old deck that was in poor shape. I dropped an occasional coal and left burn marks too. When our home insurance underwriter pulled out of our State last year, we had to get new homeowners insurance..... And they would not give it with the old deck. Or the old AC unit. They didn't even want to with the existing fence or the existing roof.
My solution to grilling/ smoking on the new $$$$$ deck....was to build a 12x12 covered area in the yard adjacent to it right at the bottom of the steps. The roof was easy The flat paver surface on mildly sloped ground was a lot more work. But 2 yards of dirt, 1/2 yard gravel, 1/2 yard sand, 2500 lb pavers , quite a few days of my time later....its pretty decent place to cook rain or sun, and clean fish. Lighted for nighttime too.