Pour 1 cup water into a 6-quart multi-functional pressure cooker (such as Instant Pot) and place a trivet inside.
Set out 4 wide-mouth pint-sized canning jars and place 2 tablespoons vinegar into each one. Add 10 drops of food coloring of desired colors into each jar. Carefully place 2 eggs into each jar and fill with water. Set jars on the trivet.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 5 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 1 minute. Unlock and remove the lid.
Use tongs to remove the canning jars and drain water carefully. Transfer eggs to an ice bath and let rest for 5 minutes.