Without knowing what the make / model of the bike is, we can't really tell what kind of bottom bracket it has.
Most kid's bikes have what's called a 1-piece crank, where the crank arms and spindle are a single, Z-shaped piece of steel.
This type does use a large nut on either side of the BB to retain an open-cage ball bearing.
Bad news, is that this type is not 'sealed' and water and dirt can get in. It also doesn't have much grease in it from the factory.
Good news, you can easily open up one of these type BB with a large adjustable wrench, clean all the old grease out, and repack it. I use what's called Marine Grease. It's intended for boat trailer wheels. It's cheap, waterproof, and can be found at pretty much any auto parts or hardware store. One good repack is probably all that bike will ever need.