Install softwares on other partitions
In general, OS X applications can run from anywhere. Depending on which R distribution you install it might run just fine from an Application bundle or you will just have to adjust your $PATH variable to place the executable files where they can be found.

You probably have a more specific install error that's causing your issues. Perhaps listing the exact version of R and where you got it / what steps you are following would allow us to help you better. (Ideally you would list the OS on Mac and the exact error message or what you are seeing that makes you think the installation failed.)