Disclaimer: This is a shameless plug for ffbinaries Node module and ffbinaries.com API I created.
I was looking for the answer to this a while ago and couldn't find anything useful. I decided to put something together myself and thought I'd come back here in case you still need it.
I created ffbinaries downloader to achieve this. I just started this two nights ago so might be still lacking but give it a try.
Still very much work in progress, currently (at 0.0.12) it doesn't set permissions on the file yet but it downloads the required binaries just fine.
Edit:
ffbinaries has reached version 1.0.0 milestone a while back - nice, stable and it does set permissions correctly :)