You can just book a weekend in a hotel spa resort somewhere. Hiring a travel agent will give you access to more discounts, more packages, more freebies. Schedule your honeymoon after/before peak season.
Consider alternative airports, you can fly in or out of a smaller of farther airport to reduce your airfare. Use your Frequent Flier Miles on your budget honeymoon. Another surefire way to have discounts or get freebies is to brag that you are on a honeymoon.