I receive a number of csv files from a third party on a regular basis, it could be 1 it could be 20 and they'll never be the same file names...
You should be able to handle this easily with a Foreach Loop Container that's setup using a Foreach File Enumerator. What I typically do is use this pointed at a specific folder, then the last task in the container is to move the file I've just done into a processed folder.
...The records all end with a comma which causes a problem when I try to load in to a sql table as sql is expecting there to be another column...
I wouldn't bother trying to script removal of the commas, this seems like extra work. If you edit the flat file connection in the SSIS connection manager, you should be able to have an extra column in there that just isn't mapped to anything in your data flow destination task. You may see a yellow triangle in SSIS warning you that it isn't mapped, but it will still run, no big deal.