Painting corroded 9V battery contacts with vinegar
Using vinegar, petroleum jelly, or glycerol to clean the contacts would leave some residue.  Vinegar might dissolve it somewhat more quickly than water, but you have to be sure you get all the vinegar off the contact, or it could cause more corrosion.  Petroleum jelly - I think someone was kidding you.  Vinegar &amp; petroleum jelly don't mix.  

Much easier: use a small piece of emery paper or steel wool to grind the deposit off.  Keep sanding until the metal is shiny.  Use a damp rag to remove the powder.  Don't let the ground-off powder fall into the circuitry.  

Edit:  added steel wool.