The best way is to use WFS service, with TIME parameter defining the relevant time range.
Example is shown here.
Note that you can also use MAXCC parameter (maximum cloud coverage) in this call to filter for cloudless data.
As a result you will get a list of all available scenes for the chosen location in JSON format (or XML if set so). Some of the dates may be duplicated if there are two scenes available in the area. You should simply ignore these duplications.