Close Mail in both machines.
In the computer where your signatures are, go to your user library (in OS Lion this is hidden, but you may access it by holding down the option (alt) key while clicking on "go" then you will see the library item in the list. Another option to access it is to go to finder, click on "go", select "go to folder" and paste this: "~/Library"
Once you are there, go to Mail - > v2 -> MailData
You will find a folder called "Signatures". Copy this folder.
Go to the same locatin in the other machine. Make a backup copy of the "Signatures" folder and replace it with the other machine's folder.
Open Mail and check everything is running.
Best