This article is from the Stardates in Star Trek FAQ, by Andrew Main firstname.lastname@example.org with numerous contributions by others.
Neither of the periods of stardates discussed above gives a satisfactory date
for ST:TMP. It is therefore necessary to have an intermediate period of
stardates to link the two. It is possible to make this link with a single
intermediate period. This period must use up stardates much more slowly than
either of the adjacent periods.
This intermediate period can have a rate of about 0.156u/d at the most. To
have a rate any higher, this period would have to extend into ST:TOS or beyond
STII:TWOK. It would be possible to use a rate of 0.15u/d (which has the
advantage of making a standard 8-hour shift exactly 0.05 units long), but this
makes the day length messy. (3u/d or 0.3u/d would be more manageable, but it
isn't possible in this case.) The most logical rate to use is 0.1u/d.
Now to place ST:TMP... It must be a fair bit more than 30 months after "All
Our Yesterdays", ideally in late 2271. To make the changeover point from
ST:TOS stardates to this period an exact midnight -- it would be madness to do
otherwise -- it must be a multiple of 5 units. This means that moving it one
day forward or back changes the date of ST:TMP by 49 days, because the
stardate rates differ by a factor of 50. The most reasonable date possible
for ST:TMP under this limitation is 2272-01-10, with the changeover at SD
7340.0 (2270-01-26). This is not quite in 2271, but close enough not to cause
problems with later dates.
And for the second changeover... It turns out that fairly sensible dates for
STIII:TSFS and STVI:TUC can be obtained by putting the second changeover at SD
7840.0 (2283-10-05) -- exactly 5000 days (500 units) after the first
changeover. This makes it all look designed. This puts STIII:TSFS at
2285-10-14, consistent with the Chronology. It also makes STVI:TUC
2292-12-19, which is not quite the conjectural 2293, but is close enough.