Don Kagin's degree is a PhD - he got several professors to work with him and did his dissertation on California Gold - basically it was his book or his book was his dissertation.
Jonathan Kern's degree is a BS in Numismatics but basically it's in Metallurgy. He was in school, left and returned - slightly older than other students and allowed to do a lot of independent work.
Numismatics is a more accepted discipline in Europe - it should be here, too. Several colleges offer courses - no one a degree (except under special conditions like Don and Jon). Ted Buttrey has taught at Michigan, Alan Stahl now at Princeton came from the ANS and taught a semester at Notre Dame.
Princeton, Notre Dame, Cornell, Bowdoin and Harvard all have significant collections - about 10 other have some very good collections - so courses should be possible.
I believe Jon Kern's bachelors degree in numismatics emphasized metallurgy and mine was more historically oriented, taking courses in the College of Arts and Sciences which included independent studies from the Greek and Roman Department (Ancients), Probability and Statistics (Math Department), and various Political and History Department courses. I believe three of these papers were eventually published in The Numismatist and I would be happy to send copies to anyone interested in them.
I believe Stanley Appelbaum of First Coin Investors (I may have the wrong spelling) and later Pine Tree Auction Company located in Rockville Center, N.Y. was the visionary behind the Adelphi program, but I don't remember they awarding a formal degree.