I have the same problem as the OP. Even though I have several psp games on the transfer list they do not should up in the content manager. I was able to transfer ClauDun and Ape Escape but not any of the others. I also cannot trnasfer the games saves and saved data that I have on my PC to the Vita. It just tells me that there is no content there. I have been trying to do this off an on for days now.
Transfers from the PS3 are controlled by the Vita's Content Manager. If a PSP title doesn't show up there, it is currently not compatible.
Alternatively, you can download purchased PSP games directly from your download list in the Vita Store.
Also, the downloaded PSP game must be in the "bubble" on the PS3, i.e. uninstalled, if you "install" it on the PS3 it can only be copied to a PSP not a Vita.
Here is a list of what PSP/PS1 games that can be transfered over to your Vita:
Not all games are supported unfortunately.