Tell us more.
What kind of FPGA really? Maybe you can integrate the HDMI encoder and serializer inside the FPGA instead, as BrianHG suggested. Or maybe you can't. So tell us what FPGA you have in mind.
If you really need an external chip, you will have a hard time finding something requiring fewer IOs. And, there is no magic anyway: the narrower the data bus, and the higher the data rate for a given pixel clock frequency. So... how fast could you pump out data with your FPGA? But anyway, I for one do not know of such a chip with a narrower data bus.
Now for the obvious trick: the TFP410 supports several modes (12 bits/pixel and 24 bits/pixel, the latter can use a 12-bit data bus or a 24-bit data bus...)
The question: do you really need 24 bpp? Can you do with less? In the latter case, you can just tie several data bits together, and save a few IOs.
For instance, if 12 bpp is enough, you can use the 24 bits/pixel, 12-bit data bus mode and tie D0/D1, D2/D3, ... D10/D11. Thus you'll only need 6 IOs for the pixel data instead of 12.
Likewise, if 6 bpp is enough, you can wire the data bus in the same way and use the 12 bit/pixel mode - with only half the data rate required compared to the above.
You get the idea.