It seems like everyone here is talking around the real answer: You cannot run an older Mac OS on a new Mac, it does not contain the drivers for the new hardware. Unlike Windows, which is certainly not a "doz-ing" off OS, you cannot install drivers into an older Mac OS to support new hardware. I can install Windows XP onto any new Windows 7 PC with the proper XP drivers if they exist (which of course they may not).
That said, there is a lengthy thread on here on installing Mac OS 10.6.8 onto the new Mac Mini. Snow Leapard 10.6.8 contains drivers for the new Mac Mini hardware because it was previously used on MacBook Pro's which contained the same hardware as the Mac Mini. However, it's not for the faint of heart, and involves using a target MacBook Pro and several Snow Leopard disks. Even then, it didn't work for some people. So your Rosetta applications will probably require a separate Mac, e.g. a refurbished 2010 Mac Mini for example.