Enter first the Aperture 3 serial number, because it is Aperture 3, and then it should ask for the Aperture 2 serial number.
If your old Mac is running Mavericks, you could upgrade to Aperture 3.5. You should see the Update at the App Store in the Updates tab. But Aperture 3 needs to be installed in the Applications folder and simply be called Aperture, not Aperture 3 or similar.
In some countries it was necessary, to set the primary system language temporarily to English U.S. and the region to U.S., then to restart the system, for the Update to show at the AppStore.
If you can update your Aperture on one of your Macs to Aperture 3.5, your licence will be converted to an AppStore licence, and you will no longer need your serial numbers. Then you can install or reinstall Aperture from the App Store on any of your Macs, without needing the serial number.