Jon and Daenerys being conceived on the same night in the play is not a timeline error.

It was a plot device used to illustrate the concept that "when a Targaryen is born, the gods toss a coin." The intention was simply to emphasize, subtly, that one of them is the Prince That Was Promised and the other isn't; this doesn't contradict the fact that they were born on different days in the canon, nor does it conflict with the idea explored in the books.