Perhaps the simplest tattoo, but no less meaningful, with your child's name placed over your heart or at almost any other location. There are hundreds of styles and fonts to choose from when considering a scripted tattoo, so you should be able to find what you are looking for. But to make the tattoo even more unique and meaningful, you can have your child write his or her own names on a piece of paper and use that for the script, that is, if they are old enough to write.
A tattooed portrait of your child as a baby or at any age can be a pleasant memory and reminder of your love. You should keep in mind that portrait tattoos often must be large in order to show adequate detail when considering its placement on your body. The flatter and larger the surface area, the better. These can be done in classic black and gray style or in color.
Another classic father tattoo, and maybe the most individually meaningful, would be an object for which only you and your child would understand the significance. This can be almost anything so long as it is a shared interest between the two of you. Different tattoos should represent each child if you have more than one, to best portray the indivdual bonds.
Your child's birth date can be added to any of the tattoo ideas above or be shown by itself. A seemingly random string of numbers can often be a clever meaningful way of show your love and fatherly bond. You can choose from several styles and types of number script or design your own. You can also choose to keep it simple black and gray or develop it into in extravagant and colorful piece.