From running classes and teaching hundreds of parents and babies it is not uncommon at all for babies to howl indignantly at the first sign of massage, and the worst thing you can do is grit your teeth and carry on - you run the risk of creating a negative association in their minds.
Even if your client is not emotional when they arrive for the massage, techniques used during the session may bring up feelings or memories related to an event or injury. Don't worry! This isn't necessarily a sign that you aren't giving a good massage; most people have varied reactions to touch, and some of these emotions may manifest as crying. It's important to understand that while these situations can be awkward and potentially embarrassing, they are fairly common and should be treated with respect and compassion before, during, and after a massage. Clients should not be counseled by you during these emotional situations, as this is outside of your scope of practice.