My daughters father who has only seen my daughter once is wanting visitation because I am making him pay child support. Can I make it so that he can only get her during the day and not over night until they develop a relationship?

You can't make anything. That's the judge's job. I find it interesting how many times I've heard this excuse in 20 years that the father wants visitation simply because he has to pay child support. If he didn't care to support the child, why would go to the enormous expense of trying for visitation? Even if he gets it, you can violate it on a whim, and unlike child support, there are no government funded programs to enforce visitation.

At best, the child deserves Bird Nest custody of you two.

All Children Deserve Two Parents
Georgia Supreme Court Chief Justice Leah Ward Sears has noted, children born to unmarried women and to those in cohabiting relationships “must often overcome increased risks of poverty, education failure, child abuse, delinquency, emotional distress and mental illness.”…….the lack of a father’s guidance in children’s lives is a major cause of their suffering. “Marriage is the best child welfare, crime prevention, anti-poverty program we have,”
http://www.barnesville.com/archives/266-gem-from-jim-octuplets.....html

Fortune Magazine - Fatherless Families & Crime
“Ominously, the most reliable predictor of crime is neither poverty nor race but growing up fatherless.”
http://money.cnn.com/magazines/fortune/fortune_archive/1992/08/10/76732/index.htm

Stanford University - Divorce, Nontraditional Families, and Its Consequences For Children
"We know that children of divorced parents have more emotional and behavioral problems and do less well in school than children who live with both their Parent."
http://www.stanford.edu/~rmahony/Divorce.html

If his name is on the birth certificate, or he has been adjudicated in court as the father then he has as much rights to her as you do however if the child was born out of wedlock, and nothing has been to court you have sole custody of her until it goes to court I am somewhat in the same boat except I let the father see her over night which was a mistake b/c he now has her in Ky which is where he lives, and up until now hasn't let me see her.

It depends on the state you live in. Where i live you have to first establish custody (full, joint) and then visitation rights. You can set it up the way you want and then have it changed down the road. Be prepared for him to attempt to act a fool. If you don't do anything else, make sure you have custody of your child!

Go back to court and request the type of visitation you want. But he needs to realize he is not paying a fee to get to visit the child, he is paying for her needs.