Couldn't you just use a smaller sized yarn and smaller needles, with your same old pattern. There isn't much knitting in these things, and if you get going and think they'll be too big/small, then pull out and start over with different needles. Just measure the circumference of the child's hand, the distance to the thumb, the length from thumb to finger tips, and then knit a swatch...use all this as a guide. I don't usually even use a real pattern...just decide the size I want and, use the same sort of instructions on any mitten pattern for the thumb and tapering ending, only scaled to the size I'm using. Pretty simple, really. This makes a mitten that is sized for the particular child, and isn't just a generic size.

There are several free child size mitten patterns at Lion Brand. You do need to register, but it is free.
They look easy. I have a Cottage Creations pattern that goes from small child to adult that I use, but it is not a two needle pattern.

Tami