My cousin is looking for an inexpensive high school on line to get his diploma. Can anyone offer suggestions?

Most online high school will be considered home school by the states school district unless it is actually through the local school for those who are homebound for medical reasons.

There are many good systems so what you mean my inexpensive, 1000 a year or 5000 a year, each can be considered inexpenisve for home schooling depending on the program.

And you did not mention if the cousin is the parent looking for something for their child or is this the child looking for something, If so they need to invovle their parents since the parent will be responsible, the parentwill have to file with the local school district and depending on the start meet other requirements

A lot of good info here
Homeschool: HSLDA-Home School Legal Defense Association: (http://www.hslda.org/Default.asp?bhcp=1)