People have already done the work to know where the music data is in games -- it's already been ripped into NSFs. So working with NSFs to figure out the format is usually easier.
Assuming both versions of Rygar have the same format for music... all you really need to do is figure out the starting/stopping point for the track. You could probably do that just by finding the track pointer tables. If you're lucky, the US song will be same size or smaller and you'll be able to just copy/paste the song in -- but probably not.
I could probably help more, but I'm not familiar with which song is "Dorago's Palace"... so....
The US Rygar NSF: http://www.zophar.net/music/nsf/rygar-
The JP Rygar NSF: http://www.zophar.net/music/nsf/rygar-jp-
Which track is it in the US and JP nsfs?