Children under 3 are not on the dining plan. They don't receive dining credits.
The only way to get a dining plan for a 2 year old is to register the child as 3 years old. This means you must buy a park ticket for that child if you are on a package with tickets, because as far as Disney is concerned that child is 3 years old. If you're not on a package that includes tickets, you'd only pay for the dining plan. Free dining requires a package with park tickets, so while the dining plan itself is at no extra cost, there is the cost incurred for buying at least a 2 day park ticket in order to get dining credits for that child.
The 2 year old can eat whatever they want free if you are going to attend buffets, all you can eat family style restaurants, fixed price restaurants or dinner shows. For the time that they are 2 I would book as many of those meals as possible. It is true that if you are at CS or an a la carte restaurant, the child would have to share with the rest of the party or your would need to buy them a meal. But the price of a few child's meals should be compared to what it would cost to buy him a park ticket.
