Let us remember that relativists always argue that there is no such thing as absolute truth, and that it is always culturally shaped and defined. Therefore, what is "true" for one culture or time period will not be "true" for another culture or time period. Relativists would cite changing laws and approaches to issues such as homosexuality and abortion to support their position.
I suppose one issue that we could point to that relativists would find very difficult to argue for nowadays would be paedophilia and child abuse. Although they could argue that such practices did occur as part of Greek civilisations and other cultures in ancient history, it would be very hard to support that view in today's day and age when the rights of children are enshrined and supported. Another issue, along similar lines, that could cause relativists problems would be that of human sacrifice. Advances in knowledge and technology mean that it would be very difficult to argue for human sacrifice in today's world.