If the spring is one of the long coils, then yes, you can replace them fairly easily and cheaply.
The best thing to do is to first weigh the garage door. You can do that by taking your bathroom scale and setting it under the door, after removing both springs. they make the springs in different strengths. After a bunch of coats of paint, the door is probably a lot heavier than it was...get one designed for what you currently have.
replace both springs even if the other one looks fine. You want the tension and strength to be even side-to-side. Also, if they don't come with them, buy the safety cables that go through them to prevent the spring from getting loose and maybe hurting you or breaking something (people have been severely injured by a broken garage door spring).
All new garage doors come with the safety cable.
The new openers also have several safety features, so a new opener might be in order while you're working on things. Most also have a remote that is much harder to clone or steal and gain access to your house.