A solvent for for ballpoint pen ink is alcohol. Denatured alcohol is best but rubbing alcohol or even cheap aftershave will work. There might be a reaction with the finish that is on the wood so do a test by putting some alcohol on a rag on a hidden area of the furniture to see if the finish gets sticky. If it doesn't, use a clean rag to transfer the alcohol to the ink and wood. Try to use a blotting action more than a rubbing action as much as possible. The alcohol is flammable so don't use it close to sources of ignition. Also let any rags that you used stay outside and not wadded up for a day to get rid of any fumes or residue.