There are Pokedex entries that estimate when 10 of the fossil Pokemon lived: Kabuto, Lileep, Anorith, Cranidos, Shieldon, Bastiodon, Tirtouga, Tyrunt, Tyrantrum, and Amaura. Of these, all except Kabuto are stated to have lived approximately 100 million years ago, while Kabuto "has remained unchanged for 300 million years". We can also assume that Kabutops, Cradily, Armaldo, Rampardos, Carracosta, and Aurorus would have lived at the same times as their pre-evolutions, so the Pokedex provides time estimates for 16 of the 24 known fossil Pokemon.
There are Pokedex entries that estimate when two of the past Paradox Pokemon lived: Scream Tail and Sandy Shocks. Sandy Shocks' implies that it lived somewhere around 10,000 years ago, while Scream Tail's states it lived one billion years ago.
There are other vague references to time in both fossil and Paradox entries, such as "primordial" and "ancient times", but these don't provide conclusive measurements.
From this, we can conclude that most fossil Pokemon lived around 100 million years ago, predating Sandy Shocks but being beaten by Scream Tail. It would be difficult to say if this is actually the case, though, as the Paradox entries are vague and unreliable. Anything beyond these numbers, however, would be speculation.