There is a free SNTP client for PalmOS here:
http://www.citi.umich.edu/u/rees/pilot/
If you use a GPS with your PalmOS device, yet another possibility
is to use Cetus GPS (also free):
http://www.cetusgps.dk/
To the best of my knowledge, PalmOS was not designed with high
time precision as a goal. I believe either of these should be
good enough for most users.
Romain
