Wikipedia's entry on vampires implies that it is the 1922 film Nosferatu that first introduced the trope, as part of its attempt to vary the Dracula legend so as to avoid a lawsuit:
fangs and vulnerability to sunlight appeared over the course of the 19th century, with [...] Murnau's Nosferatu (1922) fearing daylight.
The entry on Nosferatu elaborates on this:
Orlok must sleep by day, as sunlight would kill him, while the original Dracula is only weakened by sunlight.
While the Vampire Literature entry makes it even more explicit with "It is only with the 1922 film Nosferatu that daylight is depicted as deadly to vampires".
Of course, all these Wikipedia references seem to be traced back to David Skal's book, V is for Vampire which, umm, doesn't really give off a particularly authoritative air, I'm afraid.
I have also searched through the works provided online in this Vampires in Text page, looking for the word "sun" through the texts, but with no luck. Perhaps a more through search for more synonyms will turn up a clue. And of course, many works there are just cited, without the full text available.