In the absence of any inherent ordering, presenting arbitrary lists of items alphabetically is usually a pretty safe bet.
Ordering by expected frequency of use can be useful sometimes, but unless you have solid data to back it up, it can be pretty subjective (and thus, not necessarily much better than random for any given user). In this particular case, frequency could presumably vary from one user's programming project to another.
Your suggested ordering also happens to roughly match the CRUD lifecycle, with which your target audience will likely be familiar. For that reason, it's not uncommon to see these particular APIs listed this way, e.g. on this REST API Tutorial.
However, if this is a generic product where not all the lists of APIs you have to show will necessarily conform to this sort of ordering, then always ordering alphabetically might still be the safest bet. If the ordering changes from page to page depending on the particular set of APIs on that page, your users will find it harder to find what they're looking for.