Silver Coin Dealer
One of the important points to check is that the dealer is a member of a numismatic association. In the US this would be the American Numismatic Association for example. In Australia or New Zealand the Australasian Numismatic Dealers Association and in the UK the Coin Dealers Directory will give a list of associations relating to coin collecting and dealers in the UK.
Europe and other areas also have their own coin dealers associations.
The Professional Coin Grading service provides a list of the US coin and numismatic associations available in the US.
So there are plenty of associations which can help to establish the authenticity of the dealer you are looking at using.
Another aspect is to understand if the dealer has a warranty or provides a certificate for each coin and is willing to accept it back if later found to be counterfeit or fake.
Check the dealers Terms of Service. If they do not have one it is probably better not to deal with that company.
Ensure they have a locatable fixed address. An email address only would be insufficient.
Depending on the coins you buy, you may wish to have insurance, particularly if you are purchasing from overseas. Ensure that the dealer provides for insurance and actually includes the insurance.
In many cases the Terms of Service are a legally binding contract which you acknowledge when you make your purchase so ensure you understand it well.
Sometimes there are attractive deals in silver coins on eBay. Check the person selling. Are they a dealer? A Power seller? Do they have a web site? Check it if so and ensure they meet the criteria above.
There are many silver coin dealers so you have plenty to choose from. All want your business and the bona fide will be happy to give you great service.