The shape of smaller bike frames means there are no fixed rules about when a bike will fit in a roof mounted bike rack. A good rule of thumb with kid's bikes is that if they are small enough to fit in an average sized car boot they are too small for our bike carriers. Most (but not all) 16" bikes will fit in a roof mounting bike carriers. Some 14" bikes will fit fine but sometimes they will be too small. Fairly basic frame holder style bike carriers, such as the Thule FreeRide and Cruz Bici rack or Cruz Race, tend to be better for smaller children's bikes.
Tow bar wheel support racks are a great option for kid's bikes. If you use a hang-on rack (where the bikes are supported by two arms), you'll need to check that there is enough space in the frame to fit the two arms.
You'll always need to remove stabilizers before carrying a bike on the roof, or on a tow bar rack.