go to walmart and buy a hudson sprayer (or the generic one). Walmart has one for $8-9, its 1 gallon. Cut the end off (the very tip where it would spray the mist) and then use it to spray in the gear oil (clean and neat). It will work trust me. Also you can attach 1/4" copper tubing to the end and manipulate it to work best for you.
PS - the walmart one has a lockable "trigger" so you can set it and walk away.
EDIT: This is also really good for the Differentials, and the Transmission! Yes gear oil, even up to 85w140, it will flow through, but at a trickle... But its cleaner and easier then anything else.