I like the basketball, volleyball, and baseball way where the noun before ball has some leeway but should be clearly identified with an aspect of the sport.
football -> tackleball
rugby -> tossball
cricket -> paddleball
golf -> clubball
hockey -> icepuck
basketball -> handball
hockey -> stickball
volleyball -> handball
rugby -> handegg
baseball -> stickball
cricket -> stickball
golf -> stickball
Hopefully this will finally appease the football literalists and make things simpler for you all to understand :)