The FDA has issued a warning about codeine use when breastfeeding. Codeine is really pro-morphine; the body converts codeine to morphine, which is the active drug (which really makes you wonder about the wisdom of giving codeine/morphine to children for cough, but that is another story). A rare but serious side effect is possible in which the baby experiences a morphine overdose. Some women have a genetic trait in which they metabolize codeine very rapidly, converting it to morphine so quickly that a larger than normal amount is present in the breast milk. This can cause respiratory depression in the infant.
The FDA is not warning nursing mothers not to use codeine. Mothers who are breastfeeding and using codeine need to watch their babies carefully for lethargy, excessive sleepiness, poor feeding or decreased muscle tone, and seek medical care immediately if the baby shows any of these signs.