I have a 2 year old daughter. Her Father has only seen her once when she was about 5 months old. I would like to receive Child Support but do not want him to have any type of visitation rights due to his drug and alcohol abuse. Since my daughter he has had 3 other children by 3 different females. What is the likelihood of me being able to get the CS without giving him visitation rights?

I'm sure that regardless of the state, him having other children has nothing to do with your case. Child support and visitation are separate issues. You can pursue child support even if he chooses not to see his daughter.

If you want to restrict his visitation rights, you will have to prove that he is unfit and would pose a danger to the child. The courts would want evidence, not just your side of the story. Even then, they may initially only allow supervised visits. Long story short, IF he chooses to fight for his visitation rights, you have an uphill battle because there has to be legitimate cause to prevent a parent from having a relationship with their child.

Excuse me for jumping to conclusions here... but it sounds as if there may also be some bitterness regarding your ex because he's moved on. I only say this, because you made a point in mentioning that he has other children with other women. Of course I think he's wrong for not pushing harder to see his daughter but think long and hard before you go through the trouble of intentionally inhibiting a parent/child relationship. This can be the worst thing one parent can do and often the children grow up resenting the parent (in this case you).

First he has to file for visits, he can do that anytime he wants no matter if you file for child support or not. He just has to file.
So if you file for child support he will have to hire an attorney and file for visits.

If he does, you will have to prove he is a threat to the child and they may not allow visits, but most likely require visits to be supervised.
But he always has the right to file for visits, regardless of what you do about child support