Charlotte Elizabeth Tonna wrote The Net of Lemons, a short story (about 30 pages in length), in 1828. The story does not contain a conversion narrative, but does contain some Jewish characters and the author does convey her belief that Jews badly need Jesus and that Christians should witness of their faith in Christ to the Jewish people.
The story is about two Christian boys and their aunt (Mrs. Dillon), who encounter a Jewish fruit merchant (Levi) and his son (Reuben). Initially one of the boys (Charles) insults the Jewish boy on the street, but later apologizes for it after his aunt and brother chastize him. The two adults engage in some interfaith theological discussion (the Christian woman claims that the Old Testament saints were Christians). The Jewish boy Reuben ends up wanting to read the New Testament.
Mrs. Dillon says to her nephews "The [Jewish] race are sadly degraded, and given over to a covetous, infidel, spirit, but ... (p. 25) ... God "will subdue their iniquities, remove the stony heart, and put a new spirit within them...." (p. 26)
The Jews are said to be in a "wretched state of blindness" (p. 27). It is the duty of the Christian, says Mrs. Dillon, to give the Bible to Jews, to witness to them, for God may again bless them as he did in days of old.
In later years Tonna moderated her tone when writing about Jews and used somewhat more subtle language to express her thoughts about conversion to Christianity. There is a debate about whether or not Tonna changed her mind before her death in terms of the necessity of Jews converting to Christianity. For example, Mary Lenard in the Oxford Dictionary of National Biography writes that "There is some evidence to suggest, however, that she eventually abandoned this conversionist attitude towards Judaism and devoted her efforts towards fighting antisemitism." I agree with Lenard that Tonna was concerned about antisemitism, but I don't think that there is any evidence that she ever lessened her efforts to convert Jews to Christianity.