Okay, so George III's daughters didnt have kids due to most of them either remaining unmarried or only getting married in their mid thirties. Several matches were proposed for some of them, namely second-in-line princes to Sweden, the Netherlands and Denmark.
So, here's my proposal as defined by OTL marriage offers.
HRH Charlotte, the Princess Royal marries the future King Frederik VI of Denmark
HRH Princess Augusta marries Prince Adolf Frederik of Sweden (as he originally offered)
HRH Princess Elizabeth marries Louis-Philippe d'Orléans (she was forced by Queen Charlotte to decline this proposal) or Landgrave Friedrich of Homburg (as OTL, just in the late 1780s-early 1790s, not 1818)
HRH Princess Mary marries Prince Frederik of Orange (brother of Willem I of the Netherlands)
I'm not sure about who the Princesses Sophia and Amelia might marry. Maybe Charlotte's OTL stepson, King Wilhelm I of Württemberg?