Assume I have to use a Roman numeral to denote an ordinal number. Is it more correct to affix “-th” to it or not? That is, should I write “XIX century” or “XIXth century” to mean “nineteenth century”?
I have never seen someone write "IIIrd" or "Vth". In addition to being (subjectively) ugly, it is basically unheard of.
We write "the XXIII Olympiad" and pronounce it as "the 23rd Olympiad".
We write "Napoleon III" and pronounce it as "Napoleon the third".
So in my opinion you should write "the XIX century". (If you can't write "the 19th century")