No, we wouldn't say that.
If it is clear that you are referring to coffee, you would just call it dishwater.
It would be helpful if you would provide some context so we could better advise you.
I am rather perplexed by the use of "bon" in "Je bois un bon café à l'eau de moppe..."
@Reynald & @snarkhunter: In my post #2, the link is to "Les mots québécois du quotidien..."
For some reason, the "QC" (for québécois) following "moppe" did not copy when I did my copy and paste.