You can paint your counter top but it is a temporary fix. Even if you prepare and paint it properly it will only last you about 1-2 years. Spray paint would definitely NOT be the way to do it. You will need to de-grease it with a product like TSP or M83, then sand, then prime with a high adhession primer such as Fresh Start, then you can paint with an oil base paint. Also, you will need to let the paint cure for 24-48 hours(depending on humidity) before you can touch it.
IMO you are better off the replace the counter top. You can get nice laminates that aren't to expensive. I did mine last year for $450 and my counter top as not a simple design. In total I have 21 linear feet with a bar sweep, a mitre and 4 finished ends. Also, I paid extra to have the backsplash removed to make it look more modern.
