The original system would have been Snow Leopard. I suppose you know that the commercial installer for Snow Leopard, which is pretty easy to find, will not install, as it is the public release build for version 10.6.3. Your 2010 MBPro came with a special build of that version, or maybe 10.6.4. You would need the original DVD that shipped with your MBPro (you probably already know this 😎 )
Another option for you, if you have an older Mac that you can use, is to install the commercial version of Snow Leopard, using the older Mac for the install. Use the SSD from your "newer" MBPro as the destination, either by using Firewire target disk mode to give access to your second SSD through your older Mac, or simply remove the SSD, and install connected to the older Mac with the drive installed in an external USB enclosure. Update the Snow Leopard system to 10.6.8, and install in that 2010 MBPro. It will be usable now, running Snow Leopard.
And, you won't have to work with a possibly-flaky DVD drive for the system install - and you don't need the special build of 10.6.3/4