In Godwin's 1796 list for 1780 and also in the 1794 version, between Munnings and Harmer. There is a person record in GD website for 'generic' White but the entry in the 1796 list has not been coded to it. 22.1.1789 White (after Warton and before Kippis) at Robinson's / 24.1.1789 White (after Warton and before Kippis) at Hamilton's / no more for 3 years
I have done some research on the White entries in Godwin's diary but I'm still some way from identifying them all, I will probably add to this entry later but for now I'll discuss who the White in 1780 and the White in 1789 might have been. The 1780 White seems likely to have been someone connected with Godwin's ministry in Stowmarket, Suffolk as it comes between Leonard Munnings and Thomas Harmer, both of whom he met in that connection. But the only clue I have at present is Nathaniel White (Surman Index 1730-1783 dissenting minister Old Jewry London 1766-83), his will PCC 1783 of Hackney. Dr Joseph White DNB 1746-1814 can be counted out as he appeared in the 1796 list for 1787 as Dr White. The White in 1789 at two publisher's dinners was quite likely James White DNB 1759-1799. He may also have been the White satyric of 12.7.1794 at (Joseph Clayton) Jennings', White's Hints, an anti-slavery tract of 1788, uses Swiftian satire, though Godwin might have meant satyr-like as he spelt it with a y. Robinson published his John of Gaunt (1790) and his Original Letters of Sir John Falstaff (1797) and Luke White, the Dublin publisher who was also present at both dinners, was one of the Dublin publishers of Earl Strongbow (1789). Other of his works were published by a variety of publishers including Debrett and Dodsley. In 1780 he had just graduated from Trinity College Dublin and didn't have anything published until 1787 so he seems unlikely to have met Godwin then.