Well, it's actually impossible to pin down an exact date.
"It was the 23rd century..."
"...and headed for the Sirius sector..."
(Intro movie)
So, we know it's some time after 2200AD.
Also, it's the year 816 AS, ergo, add 816 to the date.
3016
However, where did the Sleeper Ships end up?
Now, there are lots of "we might not actually have reached/may have overshot Sirius" theories.
BUT...5 ships all arrived in the same place, within about 50 years? Sounds like more than coincidence to me.
So, lets assume we DID reach Sirius...how fast did they go?
In the intro movie, you see the ships cruising through the debris and laser blasts at a regular, fairly slow, speed. Then, suddenly, they speed up dramatically. They even seem to be pushing the light barrier.
But, we have no accurate data on their speeds, we can only guess.
But, what we DO know, is that we are at 3016AD plus time taken to reach sirius from earth.
Personally, I think 816 AS is a good enough time stamp as any.