A covenant of marriage (a verb with an object) means,
You promise to love each other for better or for worse. You promise to love each other for richer or for poorer. You promise to love each other in sickness and in health. You made a promise and promises are not to be broken.
If you say to each other that divorce is not an option, you will work harder at fixing whatever problems you may have.
You also need to remember that the covenant you entered also involves a third person-God. If you are having problems, go to Him and His Word. There is much wisdom in how to have not only a good marriage, but an abundant marriage within the pages of the Bible.