Yeah, I thought about it too. In my opinion the timeline in this series is just messed up specifically thanks to Driver San Francisco mostly, because they didn't really acknowlodged the stories of the past games, and just threw in the names of the old characters without knowing their backstories very well. I honestly think that San Francisco is a reboot of the series, and therefore not "canon" to the original three-games story arc, but this is just my opinion.
In my opinion the first Driver is in the very late 70's or very early 80's, since the cars look right for that era. Tanner looks young, in his late 20's or early 30's. One can think it's in 1986, because Miami features it's Metromover, which was completed that year, but I don't think that's true since the ambience seen in the .fmvs and of the games in general doesn't feel the late 80's at all. I think it's simply an anachronism error made by the developers, because it's cool to have a chase with the monorail (The Informant) instead of other cars for once.
As for Driver 2, I think it's in the early to mid '80s. The game doesn't feature any cellphones and the calls are still made using landlines and rotary payphones, also the vehicles and the general ambiences of the .fmvs show you that it's no longer the 1970's as compared to the first Driver but somewhat later than the first game.
Driv3r, it's in 2004 since it features cellphones and somewhat modern cars. It features modern day ads and the ambience of the game cutscenes are styled to resemble the TV police investigation drama series of the early 2000's, like C.S.I. or so. While the first two games are inspired by the '70's/80's car chase movies, such as... The Driver!
Parallel Lines is probably the first games that clearly states which era is in, despite being made by Ubisoft and not by Reflections Interactive, it doesn't modify the original story arc since it features a new protagonist - T.K.
I think Parallel Lines and thefore Driver '76 happens before or just right after the first Driver, so it's up to you to decide which game is the first one of the series. If Parallel Lines happened first, then you need to consider that '76 is the first one in the series since it's a prequel of Parallel Lines.
Lastly, there is San Francisco, which states it takes places some months after Driv3r, but that's clearly false since the game screams 2011 all over it, cars, ambience and feels like a TV police drama of the 2010's. As I stated above, it's a reboot because Ubisoft remade the characters from the ground-up; like what the hell, Ubisoft, Tanner is now in his early 40's in 2011, so in the first Driver how many years he had, five? It's ridiculous. It's still a great game though.
Since you ask for a chronological list, here's my personal one.
- Driver '76
Driver San Francisco Wii (it's stated that it's a prequel of the first Driver, but it messes up the story even worse than the normal Driver SF. If you consider San Francisco to be in the main story arc, then SF Wii events happen before Driver.)
Driver Parallel Lines (1978 era) or Driver
Driver Parallel Lines (2006 era)
Driver San Francisco (reboot, doesn't really fit with the original story arc).
Driver Speedboat Paradise.
This is just my theory, and therefore take it with a grain of salt.