I have recently been sent cola papers from child support office.
If they know that I no longer live in the same city making the same money as when the initial child support order was issued. Why don't they simply adjust my cost of living via computer? I can't run back and forth to court AND work to pay child support.

What did the papers say? Was it a summons with a court date? Did it indicate the amount they want to raise the support? Also ANY question on law needs to include your general locale as laws vary by area.

It may be that the law where the support order was issued does not allow an automatic adjustment but requires you be given the opportunity to fight it. If the amount of the increase is included in the paperwork, then send a letter to them agreeing to the increase. You can also ask to appear via telephone.