They have at least maintained diplomatic relationships
In DS9: Broken Link Garak states that:
GARAK: Ah, yes. The assassination of Proconsul Merrok of Romulus. Such
a tragedy. I met him once, a few weeks before he died. I was working
as a gardener at the Cardassian embassy during the [missing part].
ODO: You were a
gardener on Romulus?
GARAK: My specialty was Edosian orchids.
Beautiful but highly toxic.
ODO: As I recall, Proconsul Merrok was
poisoned.
GARAK: Funny, I don't remember that. But then again, so
many Romulan dignitaries died unexpectedly that year.
From this quote, we can conclude that Romulans maintained more formal relations with Cardassians than with the Federation (with which Romulans haven't any contact between 2311 and 2364). There was most likely a Cardassian Embassy on Romulus, as neither Odo, nor Dr Bashir, who was also present, are not surprised by this fact. We might read between the lines that Obsidian Order may have been responsible for the assassinations on Romulus . This may suggest that they were not allied, and only maintained diplomatic relations.
I will exclude the Tal-Shiar/Obsidian order conspiracy and cooperation, as it was not an official arrangement between the governments, and, although not the part of the Dominion War itself (depending on the definition), it was definitely a prelude to war and will not satisfy the limitations of the question.
