I cut small-diameter pvc pipes the correct lenght to push down between the cushions and back of my sofa as well as between the cushion and arms. Nothing will keep a slip cover straight forever but the pvc pipe worked better than anything else for me.
My mother used very tightly rolled newspapers pushed between the back and the cushion of the chair. Good luck
Does the cover have a ruffle or pleat around the bottom? If so, take the cover off and sew a piece of heavy fabric tape around the top of the ruffle seam. Then take a staple gun and staple the cover to the chair. The tape keeps the cover from tearing.
Roll up some magazines or quite a bit of newspaper (shorter side) and close them shut with duct tape or masking tape (something heavy duty)and stick them in the back and sides of the chair (not visible, one on each side, one in the back, although you may not overall need that many, experiment). This holds the covers in place much better.
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