Set the Instant Pot to Sauté and melt the coconut oil.
Add the cheese, garlic, cilantro, cayenne pepper, cumin, oregano, black pepper, salt, and tomatoes to the Instant Pot, and stir thoroughly.
Once combined, carefully crack the eggs into the mixture, maintaining the yolks. Make sure they are spaced evenly apart.
Close the lid, set the pressure release to Sealing, and hit Cancel to stop the current program. Select Manual/Pressure Cook , set the Instant Pot to 1 minute on high pressure, and let cook.
Once cooked, perform a quick release by carefully switching the pressure valve to Venting.