Well there is no canon explained answer to this however using available info we might extrapolate a plausible ship that Picard may have served on.
According to this bit of "non-canon" it was also a Miranda class. However here is more info.
This was a list of ships named Reliant in Starfleet history according to the blueprints.
Now looking at these registry numbers the number for the constellation class and ambassador class doesn't work with established canon registry for those ship types. If we want to have some fun however the 22699 is a good fit for a Miranda class.
Yes another bit of info aout there gives the second Reliant NCC-26450
So in my opinion if we take this info as semi-factual the ship Picard served on was either a Miranda class ncc-22699/26450 or perhaps an excelsior class ncc-2460/44686. I admit it isn't much to go by but until Mike Okuda and co. decide to re-write a comprehensive registry list for all starships this is the closing thing to an answer I can find based on an answer for you