Many authorities hold that one should politely decline or withdraw from being kvatter in this situation. Others state that the couple should work out in advance an arrangement to put the baby down momentarily (on the pillow) on a surface such as a table. Another suggestion in a similar vein would be for a third person to take the baby in between husband and wife.
Some rabbis permit passing the baby by having the wife hold two pillows, with the husband taking off the top one. There is a record of an old custom in Hevron to pass the baby directly in this type of case, being very careful not to touch.