I installed a clean copy of Yosemite on an external hard drive, which I cloned to another Mac using the demo of Carbon Copy Cloner. When trying to troubleshoot something on that Mac I discovered that it had no recovery partition. Is there any way I can create one
There is. Before I walk through it I should tell you that this is expected behavior. When Carbon Copy Cloner 4 clones a bootable drive to another drive, it doesn't create a recovery partition in the same way that the OS X installer does. Instead, it creates an archive of it and places the archive here: /Library/Application Support/com.bombich.ccc.
This archive provides you with the means to install a recovery partition on the drive--and you can do it while booted from that drive. Just launch Carbon Copy Cloner again, click Show Sidebar in the toolbar, and select the affected drive in the Volumes list. Information about it will appear to the right.
ccc restore partition
Once you've cloned your drive you can easily restore the recovery partition with a click of a button.
Click the Recovery HD button at the bottom of the window and a sheet will appear that explains something about the necessity of the recovery partition. If you'd like to install it, just click the Create Recovery HD button at the bottom of the sheet. Carbon Copy Cloner will unmount the volume, resize the main partition to make room for the recovery partition, install the necessary software, and then remount the volume.