I have a Hot Dog Stand. I use chopped onions every day, can I re use the left over chopped onions the next day? The onions are in a container that keep them cold all day long. Some days the onions have a lot of liquid in the bottom, is that a problem? I do not want to get anyone sick.  
This is a good thread to read about storage time for onions after they've been cut.   There are also some ways to attempt to keep an onion fresh.   If you're cutting your onions to serve then Joe is correct in stating that you'll want to adhere to local health codes and possibly even consider cutting your onions to order or only cutting a small amount and adding to it as needed- any good customer would prefer a fresh cut onion to an off, cut up cup of them anyway, right?  It's also prudent to remember that in nearly all cases you cannot see whether or not a food has gone bad entirely, but since you stated there is a watery liquid in the bottom of your onions it sounds like there are some visual indicators.  Just remember: If in doubt- throw it out (especially when you're serving it to the public)! 