Well, it's been a few years since I worked that one out, I'll try to remember...
We'll have to make a few assumptions in regards to where the sun stands at the time you see it rising or setting: using the formula for line-of-sight range (eg. range of a VOR, VHF...) and making the correction from a known sunrise/sunset table.
1- If you fly at, let's say FL300, that would be 1.23x(sqrt of 30000)= 213 NM. This means the sun would rise about 213NM away from your present position.
2- The earth day being 24 hours, we have 360/24=15. So 15 degrees an hour is our rotation speed, so 1 degree equals 4 minutes.
3- Next, you correct your line-of-sight distance for latitude, to obtain degrees/minutes of longitude, so if you fly along the 45N parallel for example, you apply 213NM / (cos 45)=213/0.707= 301. Attention, the 301 value is no more a distance, but is the number of minutes of angle at your present latitude (since 1 NM equals 1 minute of angle of a great circle, corrected by the cosine of latitude).
4- You then convert the result in degrees, then in minutes of time: 301 minutes of angle equals 301/60= 5 degrees. Since there is 4 minutes of time for every degree, you get 5x4=20.
The end result is 20 minutes. So the sun will rise 20 minutes earlier and set 20 minutes later at you position than what it's showing on the almanach (Jeppesen for example). Any latitude less than 30 north or south, you can disregard the Cosine correction, as the numbers change very little (cosine 30 is roughly 91%).
I have tried this method a number of times years ago when flying cargo for DHL, it works quite ok, max error I ever got was about one minute. Of course it is easier if you fly a northbound or southbound track, because you don't have to calculate the estimated position of the aircraft in regards to longitude, but with GPS nowadays, you can easily estimate any position you choose along your route.
I hope this is what you were looking for, anyhow, comments and corrections are welcome.
Flex