You need a piece of 1/32" gasket material used in piping that is reinforced to take the pressure. I super-glue them in and cover them with duct tape. I tape them because the glue makes the edges of the gasket stiff and it will fret through the tube.
I have only used a tire repaired this way on the rear, but I never had one fail.
I have a Panaracer Parcella with a cut in the side wall and it has over 3500 miles on the patch.