You can paint a tub

[Handyman]

But I would not advise it. There are professional tub refinishers that will give you a more even coat. Just look in the yellow pages under tub refinisher.
You may also want to take a look at this site: http://integritycoatings.com/ They give some pretty good information on what you have to do to paint ceramic tile or bath tub; as you will see there it is not an easy job. But they give out a free sample. If nothing else you probably should have a professional tub refinisher in your area estimate the job. It might be worth it to have them come do it or you might just p/u some stuff called “Klenks” which you can brush on , but it will not look as good or last as long.
Good Luck.