As a tattooist i personally wont tattoo anyone who is pregnant or breast feeding ... new mums are more likely to contract infections your skin is still being flooded with hormones and it will be more painful on top of that there is very little research into the effects of tattoo inks and what might be passed on to your baby either through the placenta or breastfeeding. You may find a tattooist that will do it but i think you need to think about the pros and cons first
OK, I hate when people bring up HIV or hepatitis Lol. Go to a reputable tattoo shop, make sure they have gloves on and open the needle in front of you. And as far as whether it's safe while breast feeding... the reason they say not to while pregnant is because of the risk of infection. Since it's a open wound and all. So I would say since your baby is out it's okay. Just keep your tattoo clean and watch for infection and stop breast feeding if you get one. Maybe store up milk just in case.
I wouldnt. You have a small chance of getting HIV or Hepatitis from tattoo joint so why not wait a bit to get tat until you are done breast feeding