Combine flour, salt and pepper in a plastic bag.
Beat the eggs in the bowl. Combine Panko crumbs and coconut and spread it out in a large dish.
Shake the shrimp in the flour mixture plastic bag and let set for a few minutes, then dip the flour coated shrimp into the egg mixture, then dredge each shrimp into the coconut mixing, pressing to allow a lot of coconut and crumbs to cling.
Add enough oil into a large skillet to halfway cover shrimp, preheat oil on medium heat. Fry the coconut shrimp in batches - do not crowd them in the pan. fry about 6-7 at a time. Flip after 2 minutes and fry the other side for 2 minutes or until golden brown.
Place the finished coconut shrimp on a plate lined with a paper towel as you fry the rest.
Leftover coconut shrimp keeps well in the refrigerator for up to 3 days.
Fried coconut shrimp freezes well, up to 2 months. Reheat for 10 minutes in a 350-F oven or until thawed and warm.