In the Instant Pot, combine rice, water, oil, and salt. Lock the lid in place and select High Pressure and 3 minutes cook time.
When beep sounds turn off pressure cooker and use a natural pressure release for 10 minutes. After 10 minutes, release any remaining pressure with a quick pressure release.
Add coconut milk and sugar to rice in pressure cooking pot; stir to combine.
In a small mixing bowl, whisk eggs with milk and vanilla. Pour through a fine mesh strainer into pressure cooking pot.
Select sauté and cook, stirring constantly, until mixture just starts to boil. Turn off pressure cooker. Stir in pineapple tidbits.
Pour into serving dishes and chill. Pudding will thicken as it cools.
Served topped with whipped cream, toasted coconut, and a maraschino cherry if desired. Enjoy!