Constipation in 1yea. 1 month old is either on breast milk or formula feeding.The breast fed babies have variable stools, from going each time they are fed to no stools for two or three days you really do not have to worry about that unless baby is crancky and looks sick.In babies formula fedif there is no medical reason after evaluation by the pediatrician, you can try stool softners, but most of time it is self limited.
Apple juice, maybe. Apple juice, substituted for a bottle, perhaps once a day, will generally relieve constipation. However, you did not define what you mean by constipation. If you mean, your baby is not moving their bowels by some scheduled time, then that is not constipation. Constipation is when their stool is hard. If they are not going often, that is normal, and indicates that they are absorbing well.