I live in Texas.  My minor daughter (15 yrs old) recently had a baby
with another minor (also 15).  They are not getting married. My
daughter is going to be the custodial parent. They are both high
school students living at home. So far, I have paid for everything.
Does this boy's parents have any legal obligations in regards to
paying some type of child support. If not, are there civil avenues
that I can persue.  My daughter got pregnant at this boy's home, while
they were supposed to have been supervised by his parents.

Yes yes and yes.  One you need to go to your local social service
office and have her file for child support. Second since it was your
understanding that his parents were home and if they were and
supervising they allowed it.  Check with your district attorneys
office for your states statutory rape clairification. Since he is a
minor himself the baby should be carried under his medical insurance
that his parent provide for him. Let your insurance company know this.
 If you have no medical the state will most certainly get involved. 
The child support enforcement can assist you with this.  Check with
your local police department to and see if there is any charges that
can be pressed against the parents.  If you get any assistance from
the state for the child they will go after them.  You can also get
help from WIC for the baby at no cost.  GO GET THEM!!!