So far the best solution to backup MySQL database is here:
MySqlBackup.NET - MySQL Backup Solution for C#, VB.NET, ASP.NET[
^]
But i think, you need to use
INSERT[
^] and/or
UPDATE[
^] stetemens.
It would be something similar to below query:
INSERT INTO DestinationDatabase (Field1, Field2, Field3, ..., FieldN)
SELECT (Field1, Field2, Field3, ..., FieldN)
FROM SourceDatabase
WHERE DateField BETWEEN @date1 AND @date2