I agree with Exapno_Mapcase (why do I keep thinking his name is mapocolypse?). Congress doesn’t have power to outright ban private currencies, only their usage in interstate commerce.
A small invite-only private summer camp that only takes kids from in-state would be completely immune to federal regulation on the use of private currency (like ‘camp bucks’). They could probably get away with discriminating on the basis of race, for the same reason.
Private bank currency is different because it can be argued even small private banks have an effect on interstate commerce. So that accounts for UltraVires objection, post #8.
And of course states are independently prohibited from issuing public currencies.