My ex-wife filed for child support in our divorce. In her papers, she put that I don't see our daughter. That isn't the case. I'm in the Coast Guard, and am in another state than her. I still go to see my daughter 3-4 times a year, for a week at a time.
I'm not saying I'm father of the year, but I try. I've paid child support to date. I calculated it out that I do see my daughter 10 % of the time. I'm very aware that it won't lower it very much, but I can't financially afford to pay the amount they're requesting.

What is the easiest way to lower the payment? Is there a special form for Military status?

How much you see your daughter has no effect on how much you owe in child support. You will (likely) pay about 17% of your pre-tax pay, depending on your state. Not much is going to get that number lowered.