Declining GodParent's Invitation

Of course. One is never under any obligation to accept an invitation to do anything--whether it be a godparent, bridesmaid or anything else. However, there may be some hurt feelings if one declines; it really depends on the people who are doing the asking. In some cases, a person may ask someone to be a godparent without thinking about the fact that the person being asked simply can't do so due to holding different religious beliefs.

Of course one can decline: I've done so in the past. Since Godparents are intended to look after a child's spiritual education as a Christian, it makes no sense to have one who's not Christian. I'm also a "sort of Godparent", where I'm like an extra Uncle outside the family, with no duties other than to continue being a good friend and perhaps babysitting if they need me or similar, non-religious stuff.