I'm paying my 4yr old son health insurance, ordered by the
court of Franklin county (Columbus, Ohio) At the same time, my ex wife
has been paying it regularly, since that was the agreement on the our(
divorced) final decree (we have been officially divorced since April
2006). She does not
mind paying it since that amount already included in child support.
When our lawyers did the child support calculations, she has the
amount credited wheeras I did not get the out of pocket credit for his
insurance. Can I appeal the court decision that I do not wish to
continue making payment for the insurance, and if yes, what are the
procedures? If there's a motion involves, how to write one?

Thanks

The first person you should talk to is your local government office. 
Here is there URL to the Child Support Office.  They should be able to
help you with appealing on your own.  http://jfs.ohio.gov/Ocs/faq.stm 
However, it is never recommended to take any legal actions without an
Attorney.  Your attorney should also be able to answer this question
for you.  Good Luck

There is a sample motion to modify ( more or less) a medical support
order in How To Collect Child Support, 3rd edition, usable in Ohio. 
Here is a link to the ebook download
http://www.familiesonlinemagazine.com/child-support/index.html