Existe alguma maneira de instalar manualmente o plugin?
Não. Você precisa usar o Firefox de 32 bits e um JRE de 32 bits.
O Java não é suportado no Firefox de 64 bits.
Firefox 64-bit for Windows, by design, has limited support for plugins and users will notice that certain sites requiring plugins that worked in previous 32-bit versions of Firefox might not work in this 64-bit version.
As we’ve shared previously, Mozilla intends to remove support for most NPAPI plugins in Firefox by the end of 2016.
Fonte Firefox de 64 bits para Windows disponível
You have the 64-bit version of Firefox, where only Silverlight and Flash Plugins are 'whitelisted'. If you need Java you need to install the 32-bit version of Firefox. You can have both the 64-bit and 32-bit versions installed, but you'll need to do a "custom" installation (on the first screen of the installer routine) and select or create a uniquely named folder - like maybe Firefox 32, otherwise the 32-bit installer may overwrite your 64-bit Firefox installation.
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