Going through the list of economies that currently use the dollar, it looks like no modern economies that use the dollar use any subdivision besides cents. In Hong Kong, the 1/100 subdivision is still called a cent, but it's no longer in circulation. In Taiwan, cents aren't used in coin form (only in financial markets). In countries like [Malaysia], the word sen is used, but it's a translation of the word cent (even though the word for the actual currency, ringgit, isn't a translation of the word "dollar").
On a historical note, however, the Spanish Dollar was subdivided into 8 reales in order to match the German thaler (the word that forms the basis for the English word "dollar"). It's not a current example, but it's interesting nevertheless.