Here are some wedding gift ideas if you are on a budget:
Go to your local wine store and ask for some ideas on special occasion wines. Just make sure you mention that in the card - example “first weekend home alone after the festivities are over celebration.”
Some plants, herbs or seeds for the happy couple to plant and grow along with.
Buy a movie gift card so they can go out and have their first official “date night” as a married couple.
Some couples post their honeymoon info on a site and you could just add a donation to their honeymoon.
If you have any ideas that I have not mentioned please be sure to leave a comment.