Well, this isn't a story, yet, but it's just my take on the 'next generation'.
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The Next Generation
Teddy Remus Lupin - April 1998
Victoire Gabrielle Weasley - May 2nd 2000
Molly Katrina Weasley - October 30th 2000
Dominique Rochelle Weasley - February 10th 2001
Louis Charles Weasley - December 5th 2002
Mitchell Robin Longbottom - January 12th 2003
Frederick Fabian Weasley - April 2nd 2003
James Sirius Potter - June 17th 2003
Roxanne Alicia Weasley - March 20th 2004
Lucy Grace Weasley - April 28th 2004
Frances Crystal Longbottom - May11th 2004
Scorpius Hyperion Malfoy - November 17th 2005
Rose Jayne Weasley - October 8th 2005
Albus Serverus Potter - May 30th 2005
Alice Pearl Longbottom - July 21st 2005
Hugo Joseph Weasley - September 12th 2007
Lorcan Newt Scamander - January 20th 2008
Lysander Artemis Scamander - January 20th 2008
Lily Luna Potter - March 1st 2008