We have an online store for Czech, and our invoices are printing things like á for the í character, and for other characters as well.
My question is, what font supports these types of characters?
It's an issue with the text encoding, and NOT the fonts themselves. The Czech alphabet set would be covered under ASCII (Latin-2 - Central European languages). http://www.ascii-codes.com/cp852.html
There's also a site that allows you to see the effect a different encoding can have. http://kanjidict.stc.cx/recode.php
Common fonts support those characters: Arial, Geneva, Verdana, Times New Roman, Liberation family and more.
I guess it's not a font's fault, but rather a software bug. The software you're using for your shop doesn't encode those characters properly. Solution would be to locate the problem and patch it or to migrate to a better software.