I think Embroidering for Children's T-Shirts . Use fun colors & funky fabrics impart a lot of spunk into plain T-shirts without adding the dismay bullet-proof embroidered shield. If possible ask the child for input on the desired color, shapes, characters &designs.Look here are some cartoon designs which likes children.
http://www.sgi-int.com/cat-2-cartoons-embroidery-digitizing-designs

For the stabilizer on t-shirts and onies for kids, I use an iron on tear-away stabilizer, it’s a medium weight stabilizer which eliminates shifting and puckering. I’m not a big fan of adhesive type backing, but it seems to work on stretchy type materials. You may have to order this type from the internet as most sewing shops don’t carry this type in stock.
Don’t know if you’ve read Florian’s Stabilizer Workbook (.pdf), but it’s very informative and handy for all users, new and experienced.

http://www.florianisoftware.com/products/*/*/7244

go to stabilizer workbook, it's in a .pdf format

As for the appliqué techniques, I personally have never been a fan of adhesive spray, however there are many who swear by it.
I feel the adhesive doesn’t allow the needle to fabric give, where at times, depending on the digitized design is necessary. Again, this is my opinion and only my opinion. Practice different techniques and find what works best for you. I mostly use wonder under on my material when doing appliqués, this is mainly done for a crisper look after the embroidery work is complete. After appliquéd item is done, I always iron (this allows the wonder-under to adhere to the fabric). You can purchase this in different weights at any sewing store.
Hope this was helpful and Keep On Stitching!!!

I would love some suggestions on embroidering baby and children's t-shirts. After looking through many forums on appropriate stabilizer and consulting my local sewing shop i purchased and used fusible polymesh stablizer. I read that medium weight stabilizer can be a bit stiff for kids shirts. I am having mixed results. Most of the time the shirt puckers during embroidery, but when I remove all of the polymesh and iron it out the puckers are gone. There are also times when after removing the polymesh and ironing the shirt the puckers are still there. Can anyone offer some tips as to what I can try? I place the shirt in rather gently without stretching it and tighten the hoop as much as possible.

Secondly, when appliqueing with an adhesive spray i notice the fabric tends to have some tears through it as if it is being pulled too hard. I am not sure what I am doing wrong.

Lastly, I have applied tender touch over my design to prevent scratchiness. I cut it as close to the design as possible, but I can still see it through a white t-shirt.

Please help!!