For clad I use a little laundry detergent, a tablespoon of lemon juice, fish tank gravel, and water. After tumbling I pour the coins into a pasta strainer to rinse.
For old coppers I use hydrogen peroxide heated with a halogen lamp. I give it a couple hours under the lamp then let them soak overnight. A very light brushing with a soft bristle tooth brush under running water the next day and some blue ribbon type coin protector. This works especially good on indian head cents but be careful on large cents or other old coppers, I only use this if the patinia is solid and shiny.
Here is a typical before pic after rinsing under a faucet...

This is typical of one with a sound patina after a soak in peroxide...

Two cent peices dug in our soil are especially difficult to clean, the peroxide does a nice job on them. Note the lime green bronze rot was just starting to form on this one.