I've had to do this a few times and haven't found a 'clever Hazel way' to do it.
You might want to turn off Hazel completely or at least pause the new folder while copying over the rules.
- Drag the new folder into the Folder listing in the Hazel window and position it under the old folder.
- Select the old folder then click one of the rules on the right and press Command+A to select all rules.
- Drag the rules to the new folder entry. As you are dragging, you should see a + icon under your cursor which means the rules will be copied instead of moved.
- Once all of the rules for that folder are properly copied over, unpause the folder
- Select the old folder entry on the left and delete it from the list
Note: While copying the rules, as you are dragging them, you can hold down the Command key and the + icon disappears. This will move them instead of copying them.
Possible bug that Mr. Noodle will need to look into is the last time I did this, whenever I moved the rules, Hazel would not update the rule listing for a long time. Even sometimes Hazel would stop responding. I would have to quit the System Preferences app and start it again to get Hazel to respond. However, even then the rule list wouldn't be updated for another minute or so. If you run into this, just copy the rules then delete the originals instead of trying to move them.
Hope this helps.