First please note that transactions are not individually timestamped, but blocks do have timestamps and this approximates the time of the transactions within. So you want to starting by using the listblocks command, passing it an {"starttime":...,"endtime":...} object. This will give you information about the blocks which are timestamped in the specified range. You can then use the getblock API with verbose set to 4 to get full information on the transactions in those blocks.
