Beat cream cheese with granulated sugar until smooth and fluffy.
Add eggs, one at a time, mixing after each addition just until combined.
Add pineapple, cream of coconut, sour cream, rum extract and coconut extract and mix until combined.
Remove crust from freezer and pour filling into crust.
Add 1½ cups of water into bottom of Instant Pot.
Cover cheesecake pan with foil and seal edges. Place the pan onto trivet that comes with the Instant Pot and lower into the pot.
Replace lid on Instant Pot and seal according to the instructions that came with the pot.
Cook on high pressure for 45 minutes. Let sit for 10 minutes, then manually release pressure and remove cheesecake. Allow to cool in pan, on wire rack for 1 hour, then cover with foil and refrigerate for at least 3 hours. After chilling, remove from pan before topping.