I am assuming that the reason CSEA is involved is because you established paternity through them?
I am in Ohio and there is a possible (not definite) way to come to an agreement. You would have to go to Juvenile Court (in Ohio, this is the court it goes through) and file and hear your case in front of a judge to sign off on. That costs money. It's an option. (and before anyone discredits that -- esp if you don't live in Ohio -- I KNOW -- I called CSEA myself to find out and that is what they told me!!!). But it's not definite. I think that might be the only way to sidestep CSEA -- unless she is getting some sort of assistance for the child. A simple agreement signed on paper between the two of you would mean nothing.
But since all of you seem to be happy, I wouldn't be too afraid of the CS proceedings. Especially if both of you are pretty much splitting responsibilities (custody/visitation, etc). That is a factor. Do a Google search and look at the equation Ohio uses. Plug in the numbers.
Now in Ohio, there is that Amendment to the State's constitution (that was passed by voters in Nov "Issue One") which states:
"Only a union between one man and one woman may be a marriage valid in or recognized by this state and its political subdivisions. This state and its political subdivisions shall not create or recognize a legal status for relationships of unmarried individuals that intends to approximate the design, qualities, significance or effect of marriage.
A guy I had a child with (we were never married or even bf/gf) is now challenging certain aspects of Child Support in this state that does have laws on the books that does pertain to effects of marriage, etc (i.e. "if parents were both married"), where those specific factors play into an amount of support being paid.