Nothing concrete was ever mentioned in any of the games. The dates weren't mentioned until the first offical timeline, which was developed during Symphony of the Night. Before then, you had several small hints about when the games took place:
Castlevania III: The 15th century according to the opening prologue in the Japanese version.
Rondo of Blood: Interestingly, you can see several gravestones in the opening movie, and one of them says "1730" or something like that, which would place the game at least in the 18th century. That later turned out to be correct.
The date for Castlevania III was probably inspired by the death of the real Vlad Tepes (1476). It's easy from that point on: you just have to add up the amount of time that passes between each game.
1476 + 100 = 1576
1576 + 15 = 1591
Etc.