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For a Clavinova this old, you almost certainly will have to record onto floppy discs.
I am looking up information on your specific model... please wait. Thank you for your patience.
Does this work:
1. Hold down the REC button and select a track using the Toggle buttons below the display.
2. Begin playing.
3. Press the STOP button to stop recording.
4. Press the Song Select to get to the SONG display.
5. Select the destination for the recorded song to be stored in (either USER, or USB).
6. Press 6 to get to the save page.
7. Name the Song.
8. Press 8 (OK) to complete the process.
? I'm not sure that follows the options on your CP303, so I am asking, Does that work OK?