I would seem a somewhat pointless to make a person swear an oath on something he does not believe in. There is little difference if he were to swear on the latest Stephen King novel, it would imply the same gravity to the oath he would be making.
I think if a person is making an oath of such seriousness as this is meant to imply - then he should be obligated to swear on the Qur'an.
Edited by Vacate, : Spelling