Hi I am never sure how to order replacement coils like these, any tips?
You’d probably start by navigating to the fixed inductor family, and entering the desired inductance value. Inductors are commonly labeled in uH with the last digit indicating number of trailing zeros, 470uH in this case.
There is a general correlation between size and current capacity, so further filtering by package/physical dimensions can roughly narrow the field. Without a part number however, a person is left to either the try-one-and hope method or reverse-engineering the circuit to determine component suitability.
This post may have additional useful information on the topic.