Your porcelain tub will stand up nicely and survive the bleach treatment that I suggest for your stain removal project. Simply put some bleach onto an old towel, and rub into your stains. The combination of the bleach and your strong rub motions will work.
Ajax cleaner is one way to get the paint off. Spinkle the ajax powder on area that is stained slightly wetting it with water first. Allow the Ajax to completely cover the stains and let sit for 30 min. Wipe with heavy duty sponge or Mr. Clean Magic Eraser.
If your tub is white, you could create a paste with a little bit of bleach and either Comet or Ajax and rub that into your tub. Let it sit for an hour or so and rinse with warm water. Be careful because this can irritate your eyes.
