A workaround would be that the schema that the JSON payload maps to has it defined as a string, and then you only map it to the canonical or internal schema which has it as a date field if it is not an empty string.
Another option would be similar the the solution in REST JSON Christmas Puzzle – Work around but to find an empty node and adding xsi:nil="true" e.g. find <StopDate></StopDate>
and replace with <StopDate xsi:nil="true"></StopDate>