If permitted, one might 'affirm' if one's religious belief prohibits 'swearing oaths': "But above all things, my brethren, swear not, neither by heaven, neither by the earth, neither by any other oath: but let your yea be yea; and your nay, nay; lest ye fall into condemnation."

http://www.kingjamesbibleonline.org/James-5-12/

I'm nonreligious, but agree with this position, as the alternative would imply that lying should be expected in all cases where no oath is sworn. Here's one small, specific, interesting piece of the history of offering an alternative: http://www.northcarolinahistory.org/commentary/161/entry