Check out this WEB page. I'll spare giving you the winning 'recipe' because it, among others, is on the page.
It's Bathroom Cleaning Tips. If you're a little clever, you can work your way back to the 'main' page for this site and get all kinds of 'tips' for lots of stuff in the home. This recipe is more 'agressive' than Lysol. If Lysol was strong enough, you'd probably buy only 1 bottle in your lifetime!!! (Sorry Lysol).
For your purposes, the recipe that's given will work on black mildew. You know, you need to eliminate the sweating so you're not getting blisters on your knees. You can do 1 of 2 things but first, understand what's happening. The cold water entering the tank is cooling the tank and the warm air in the bathroom is condensing on the tank. Hence, condensation and the dripping. Now, if this is only occurring when you shower or blow dry your hair in the bathroom, simply open the door and/or window a bit to help 'cool' the room to reduce the warming effects. If you're getting this problem no matter what the temperature is in the bathroom (showering or no showering), you'll need to insulate the tank to create a barrier between the warm air and the cold tank in order to prevent the sweating. Home Centers and specialty plumbing supply houses (see your yellow pages) sell insulation 'wraps' for this type of problem.