If an unmarried couple adopt a child and split up 7 years later, how can you establish child support?

If both of you adopted a child and you were never married, then you would file a paternity action in court.  You would include the information about the adoption in the Petition.  The court would take judicial notice of the adoption.  The court would then decide issues regarding the child including child support, parenting time, custody, cost of extracurricular activities, how the tax exemption would be divided, payment of uninsured medical expenses, schooling, etc.  It is also possible to reach an agreement regarding these issues, but I would be very careful to have that agreement in writing and submitted to the court so that no one could change their mind.  It is also important if you want the court to enforce the agreement.   You may want to calculate what your child support would be.  I suggest that you go to http://www.in.gov/judiciary/2625.htm and you can calculate what your child support would be.  I do not know how old your child is, but another issue to consider is the cost of college.  Please understand that you will not be able to get child support prior to the time that you filed your Petition.  A court may not make the child support retroactive to before the time that you file your Petition.   In calculating the child support, only use the income of you and the child's father, do not include other family members.