A portrait tattoo is a life-like rendering that more closely resembles a photograph than a drawing. You can choose a picture of your child, at any age, and have it tattooed in a portrait style to almost anywhere on your body. Just bear in mind that portraits are extremely detailed and often require a large amount of space to display adequately. Also, the flatter the surface, the better, such as the chest for men and the back for women.
A scripted tattoo, such as your child's first words or name, can be a simple design with a profound effect. There are literally hundred of fonts and styles to choose from when considering a scripted tattoo, but if your child is old enough, you might consider having him or her design the font. If you child is not old enough to write yet, but you still want to make the tattoo more personal than a generic font, you can always design it yourself.
An abstract tattoo that can honor your child is a personal object that carries nostalgia or meaning for the both of you. It can be anything, from a toy train you gave your son on his birthday or a tree you and your daughter used to picnic under, so long as it has a shared importance. The scale of the object will dictate the proper placement for it on your body and you should strongly consider using color if the color of the object is important, such as if the train was yellow or the tree was a cherry blossom.
You can add your child's initials and/or birth date to any of the before-mentioned ideas or simply represent them on their own. Again, there are numerous fonts to choose from, but having your child design the font or designing it yourself can make it more personal and meaningful. You can also incorporate the letters and numbers as an alphanumeric code underneath a bar code or on a license plate to make it a little more original.