Yes, there are a few instances of this. (Incidentally all the myths that I can think of, as the answer to this Question, feature the god Apollo.)
Perhaps the best example involving a mortal has to do with the dramatic tale of Marpessa's betrothal to Idas. Marpessa was the daughter of the Aetolian prince Evenus, who in turn was a son of Ares. As seems to be typical of a number of Ares' sons, Evenus wished to keep his daughter unwed. According to certain Iliad scholia, Evenus would compel any man wishing to marry Marpessa to engage him in a chariot-race. If the suitor won, he could marry the maiden, but if he lost, Evenus would cut off his head and nail it to the wall of his house.
Although Idas was known to be a son of the Messenian prince Aphareus, like certain other famous heroes, it was claimed that Poseidon was his real father, and this seemed to be proven by the fact that he was gifted a winged chariot by the sea-god. Idas used this chariot to abduct Marpessa. Evenus went after them in his own chariot but failed to overtake them. Upon reaching a river named the Lycormas, he gave up, slaughtered his horses and threw himself into the river, which from then on was known as the Evenus after him.
No sooner had Idas arrived home in Messenia with Marpessa than he was accosted by his own cousin Apollo, who intended to now snatch the abducted young princess from Idas. A fight ensued between the god and his mortal cousin in which, Homer's Iliad seems to imply, Idas shot arrows at Apollo and, according to Pausanias, Apollo actually managed to take off with the young woman.
For some unstated reason Zeus himself put a stop to the contest and gave Marpessa the choice between her two abductors. In the end, Apollodorus' Library tells us, Marpessa, "because she feared that Apollo might desert her in her old age, chose" to marry Idas.
Years later Marpessa did die a tragic death, but it had nothing to do with Apollo. Her husband Idas was slain in a squabble with yet another cousin of his, whereupon the widow, like her father before her, took her own life.
According to Diodorus Siculus' Library of History, the Naiad (river-nymph) Sinope, one of the many daughters of the Asopus River, was kidnapped by Apollo and taken to the shores of the Black Sea, where she gave her name to the city of Sinope (now Sinop in Turkey). There she bore him a son named Syrus, who became the first king of Syria.
The (Greek) Argonautica of Apollonius Rhodius and the (Latin) Argonautica of Valerius Flaccus, however, each tell an alternate version of the Naiad's story in which Zeus granted to her the land upon which the city of Sinope was built, because he was so infatuated with her. According to Apollonius, Zeus "had solemnly sworn to fulfil her dearest wish, whatever that might be; and she very cleverly had said, ‘I wish to remain a virgin.’ By the same ruse she outwitted Apollo" when he made advances upon her. Sinope's own uncle, the river Halys, was yet another would-be lover whose amorous attempts towards her went the same way. "Men fared no better than the gods; this woman never was possessed by any lover."
In primordial times, the goddess Hestia was wooed by her own brother Poseidon and her nephew Apollo, both of whom expressed their desire to marry her, but she swore upon Zeus's head that she would remain a virgin forever. Therefore, according to the Homeric Hymn to Aphrodite, Zeus
gave her a high honour instead of marriage, and she has her place in
the midst of the house and has the richest portion. In all the temples
of the gods she has a share of honour, and among all mortal men she is
chief of the goddesses.
Together with Athena and Artemis, Hestia was one of the three goddesses over whom Aphrodite exercised no power, because they had sworn similar oaths of virginity in Zeus's name, and he had granted them the freedom to maintain this status in perpetuity.
The final example does not end on a very positive note for the character in question. Before Persephone became Queen of the Underworld, she was a teenage goddess known simply, and mystically, as Kore, the "Maiden." According to Nonnus' Dionysiaca, Hermes, Apollo, Ares and Hephaestus all approached her mother Demeter with bridal gifts along with the request to marry Kore. This state of affairs terrified Demeter, who rejected all the suitors and hid Kore in an underground cave. The young goddess's own father Zeus, however, was more besotted with her than any of these younger gods, and he stole into the cave in the form a speckled dragon, where he had his way with the unfortunate Kore.
From the union was born Zagreus, a shape-shifting god in whose favour Zeus planned to abdicate, but who Hera assassinated. Centuries later he was reincarnated as the wine-god Dionysus, by which point Kore had been abducted by her uncle Hades, who had married her and made her his queen in the land of the dead. Cold comfort at this stage, but there indeed were no adverse reactions against Kore by the four gods who had first sought and failed to marry her.