I take it you don't have either of the first two RCTs from GOG then since both come with the soundtrack in the extras, which have identical merry-go-round music tracks (albeit titled differently).
In any case, you still should be able to get those music files if you own either of those on disc. Since I was curious about how importing music files worked for RCT3 I also found a topic about how to easily extract the music tracks from the original hard copies, which I successfully tested with my installed GOG copies. Here's what you'll have to do:
- Go to your RCT1 or RCT2 game folder and open the 'data' folder. Notice all the 'Css#.dat' files. Those are actually all the games' audio/music files.
- Make a copy of those wherever you want them and change the '.dat' extensions to '.wav'. Now they're all proper audio files that you can play with any media player as well as being good for import into RCT3, which recognizes WMA, WAV, and MP3 files.
- The merry-go-round tracks in RCT1 are Css4-Css15 (minus the 1kb files)
- While the RCT3 import instruction in the manual and posts online suggest to move custom music into a special music folder outside the game's folder, this may actually not work. For me it doesn't anyway. I had to copy the new music files into RCT3's music folder within the game data. I just put 'RCT1' in their titles for easy recognition.
- Launch RCT3 and start/load a game. Those music tracks should now be available to you for the rides from the drop-down list.