http://www.space.com/4314-length-saturn-day-revised.html
They measure some presumed solid(ish) center.
If the magnetic field axis and the rotation axis are displaced, you can
measure when the magnetic field goes by. Or by radio sources.
Jupiter day length at the poles is slightly longer than day length at
equator, but it's about 1% 9 hr 56 min vs 9 hr 50 min.
I figure the Jupiter day length (which has been given as about 10 hours
for a very long time, certainly before we sent spacecraft nearby) is
probably from visual observation of the Great Red Spot. You can easily
see it move in a not very big telescope over the course of a night.
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