Barack Obama Senior traveled to Hawaii solo and not as a part of any other group, so evidently Kenya could pay for such a solo trip or any other trips to and from Hawaii and Kenya.
I am somewhat intrigued by the potential legal issues of citizenship posed by Obama, Sr. being a de facto paid representative of the Kenyan government. His education expenses were paid by that government, and he likely received a stipend.
The Constitution precludes children born of such representatives ever being considered natural born, point blank, no ifs, ands or buts.