I am looking for an add-in, or advice on how best to program one, that
can do something like this:
(Assuming a series of past appointments it can locate and use) I enter
in an appointment for a certain day; it creates the appointment, checks
a certain number of past appointments, takes an average of the number
of days between them, and creates a new appointment that many days in
the future.

it would be nice if I could also then, shift the date of that future
appointment and have it repeat the process rather than having to make a
new corrected one and delete the old one.

Currently, I use a recurring appointment set for a certain number of
days, and just alter each instance to reflect the correct date as it
occurs. But this means that the recurrence doesn't take those changes
into account. (For example, I set it to recur every 30 days, say, and
that puts an instance on the 6th. but it actually ended up taking
place on the 5th - even if i move it, the next one will be made 30 days
from the 6th, instead of where i want it, 30 days from the 5th.)

I'm currently doing this as calendar appointments; I thought about
using regenerating tasks, but it seemed only slightly less awkward, and
I still can't get an automatically adjusting average of number of days
that way.

The important parts of this are the record of past items being accurate
and accessible, and being able to have accurate 'predictions' of the
next future event based on the average. (As you may have guessed, it's
a menstrual period tracker - most of the programs I've encountered are
awful, so if I have to make one, and it works, I'll make it available
as widely as I can.)

One more thing: however it's done, it needs to be in a format that can
sync to PocketPC 2003. (Calendar and tasks can, but I don't see
Journal.)

Any suggestions?