Most cough
and cold medications are actually okay to take with
Warfarin, as long as they don't contain any steroid or non-steroidal antiinflammatory (like Advil or Motrin). These also thin the blood, and can be a problem when combined with Warfarin.
For a cough, try something like guaifenesin, like Robitussin Severe Congestion Liquagels or Mucinex. Avoid dextramethorphan, like Robitussin DM.