Some ways to get discounts on business-class flights include using Matrix Airfare Search to find hidden cheap fares and using frequent flyer programs to earn free upgrades from economy class. Airline staff at the gate also may have discretion to upgrade seat assignments.
Google's Matrix Airfare Search can help you find Y-Up fares, which are priced like economy-class tickets but offer automatic upgrades to business class. These fares may come up in a search for business-class or higher flights; the search also can reveal regular business-class fares which are occasionally just a few dollars more than economy class.
Alternatively, travel experts recommend being friendly to gate agents and asking for upgrades to unsold business-class seats. Couples on honeymoons stand an especially good chance of getting this perk.