It says failed to initialize the download, are you not downloading it separately from the link then placing it next to the installer and running it? That way the installer doesn't even try to download it and just uses the local file. Also, the mat lib hasn't changed since Corona 9 so you can just run the Corona 10 installer and use Custom and uncheck the mat lib, which means the installer won't try to install it (but it will still work since it's already installed, if you got it successfully installed with Corona 9 before, or even Corona 8 as I don't think there were mat lib changes since then).
PS, yep, the mat lib file is the same for either C4D or Max.