Tumbling coins to clean them damages them. Electrolytic methods are to be preferred whenever possible. I have no experience with this other than high school chemistry (at which I was very good 50 years ago) so I will mention what I think I know about that. Others here will probably post on specific techniques they use successfully.
When cleaning silver, never use any substance containing chlorine or sulfur, as these readily corrode silver.
When placing coins in ionic solution, lay them on a metal more chemically active than silver (for instance aluminum foil): this will create a "battery" which will inhibit any dissolving of silver metal, and may cause surface corrosion to separate back into silver (which will remain in place) and anions (typically sulfur) which will go into solution.
Zinc is another metal often used in sacrificial electrochemistry, generally more suited to the purpose than aluminum but not so readily available to the average person in convenient foil form.
In general, electrochemical cleaning should not proceed too fast. "Too fast" may lead to safety problems (esp. generation of hydrogen gas), and high reaction rates may create mechanical damage to weak surface structure, blurring surface details.
Do not clean copper and silver coins in the same batch. The copper will tend to sacrifice itself to protect the silver inasmuch as it is more chemically reactive.
You may find ionic solutions which need no sacrificial cathode, being strong reducing agents. But be aware that some reducing agents (esp. oxalic acid) are also chelators of certain metals, so make sure the ionic solution is matched to the metal to be cleaned.
Nonferrous metal objects (for instance natural gold specimens) are often iron stained. Oxalic acid will remove most types of iron staining and will not harm either gold or quartz, but I don't know about its effects on silver and copper. Citric acid is more readily available (think lemon juice) and is completely safe to handle and will remove some types of iron staining but you may have to be patient.
As I said, I have no practical experience with cleaning coins, only a bit of theory. I post this here because I often read of things people are doing to clean coins and cringe that they may be winding up with shiny surfaces but with valuable coins ruined of their numismatic value.
Number 1 rule when it comes to old coins: don't clean 'em unless you really know your stuff! Any damage you do will be irreversible.
Number 2 rule: even if you think you know your stuff, you don't really know it until you've tried it on some non-valuable test pieces of the same type you are intending to clean. This means (if at all possible) same alloy, and silver coins have been minted in many alloys. If you use poor quality common date silver coins as test pieces, put some fine scratches in them in a pattern you can recognize (sign your signature with an Xacto knife?) before subjecting them to the test. If the quality of the scratches is degraded by the test, you don't want to use that method on potentially valuable coins.
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Okay, all this is coming from a guy who isn't into cleaning coins. I think it's good advice, but there are people here with lots of practical experience who can sort it out and expand on it. If it turns out I was full of, well "horse exhaust" on a point or two or more, please say so and straighten things out for the Fisher forum denizens.
--Dave J.