So out of curiosity, I did some checking and it seems you can make Ubuntu/Mint install software from a PPA that doesn't have the current release by editing the software source and changing the release name directly.
So in Mint, go to Menu -> Administration -> Software Sources. Then click on the PPAs button to list the PPAs you've added. Select the entry for ps3mediaserver (not the Sources one), and click the Edit URL button at the bottom. Then change the word trusty to raring and click OK. I also disabled the PPA entry for the PS3MediaServer (Sources) entry as I don't plan to install from source. You can leave it enabled if you like but be sure to make the same replacement in that URL as well. Click the Update Cache button above the PPA list. You can now close the Software Sources window and open Software Manager to install ps3mediaserver (or install it from apt-get).
It appears the latest release from source is 1.91 but the PPA offers 1.81. Reading the PS3Mediaserver.org forums though seems to indicate that the 1.91 release is having some issues so perhaps it's best to stick with the PPA release version.