If I pay for my children to be picked up from school by a transportation service can I claim put this on my income tax?

Generally you can not deduct transportation expenses for your children. An execption would be if the transportation service is to take the children directly to an after-school facility (i.e. day care), which you have the children enrolled in specifically so you and your spouse (if married) can work, and the transportation is actually provided by and billed by the after-school program. You could then claim the expense as part of your child care credit. See IRS pub 503 for more details: http://www.irs.gov/pub/irs-pdf/p503.pdf