Use the following steps to create a custom Apple Devices 60 fps destination that you can access with the Final Cut Pro X Share function.

1. Open Compressor 4.1.
2. Duplicate either the "Apple Devices HD (Best Quality)" or "Apple Devices HD (Most Compatible)" setting in Compressor depending on the quality you need.
3. Select the setting in the CUSTOM section.
4. Double click the setting name and modify it to be either "Apple Devices 60fps (Best Quality)" or "Apple Devices 60fps (Most Compatible)" depending on the original setting you duplicated.
5. Click "Video" in the Inspector.
6. Set the Frame rate pop-up to 60fps.
7. Quit Compressor.
8. In Final Cut Pro X Open the project you need to Share for playback at 60fps.
9. Choose File > Share > Add Destination
10. Drag the "Compressor Settings" icon to the Destinations list on the left.
11. A sheet will slide open with a list of the settings available from Compressor.
12. Scroll down to the "Custom" Folder and click the disclosure triangle to reveal the settings.
13. Choose the custom setting you created in step 4: "Apple Devices 60fps (Best Quality)" or "Apple Devices 60fps (Most Compatible)".
14. Click "OK"
15. Close the "Destinations" window.
16. With the project that you want to share opens, choose File > Share and then select the Apple Devices 60fps setting you added as a share destination.
17. Make any modifications necessary and then click Next and choose a name and location for the resulting file.