Combine the first 7 ingredients and mix to make a rub. Set aside.
Remove the membrane from the back of the ribs by loosening one end with a knife and grasping it with a paper towel and pulling.
Apply the rub to both sides of the ribs and place in a ring inside the Instant Pot.
Pour Coca-Cola and liquid smoke into the center of the pot.
Close and lock the Instant Pot® lid. Make sure the steam release handle is turned to Sealing. Press Pressure Cook, pressure level High, and set the time to 30 Minutes. Then press Cancel and let the pressure release on its own.
Preheat the oven to 395ºF (200°C).
Transfer ribs to the roaster and brush with your favorite BBQ sauce.
Bake for 10 to 15 Minutes, watching to make sure the ribs don't burn.