Holing out from short range usuallyrequires confidence and a positive stroke to ensure the ball holds its line. But sometimes, downhill putts require you to be less aggressive and roll the ball more gently.
A great drill to account for all different speeds you may wish to putt in those three-footers is to use three contact points of the ball with the hole as it drops in. Fast putts rolled in dead weight will hit the bottom of the cup. Medium-speed putts will strike the plastic at the back of the hole and uphill putts struck more positively will hit the soil above the hole.
Hitting three balls into the hole at different speeds will help you gain a sensation and feel for how to control the speed of your stroke and adapt to different slopes you face on the green over those nervy three footers. See the video below.