Most rulers would usually want their portrait on coins of the realm to be as flattering as possible, but in some cases, that ended up not manifesting as well as they might have wished.
I think there was a similar thread like this one from a few years back, featuring Isabel II of Spain, but here's one of my recently acquired, visually unappealing monarchs to kick off a new thread:
Louis XVIII (1814-15, 1815-24) of France, or 'the fat pig' -Napoleon Bonaparte
I also find it quite interesting, is that like James Monroe over in the USA, he was the last wearer of the 18th century fashions (check out the hair/wig on him here; and Monroe was the last president to wear stockings I think), both doing so about a quarter into the 19th century.