Here are a collection of Classic tales or references involving Satyrs & Fauns. I made up an item loosely related to the source materials.
Satyr were talented in dancing and singing, and no one understood better than them the secrets of relaxation and pastime.
--Bedrolls of resting or droplets of recuperation that allow abbreviated long rest.
Satyr appearance was both grotesque and repulsive; they had flat broad noses, pointed ears, and little horns sprouting from their foreheads, a rough shaggy skin, and small goat's tails. They led a life of pleasure and self-indulgence, followed the chase, reveled in every description of wild music and dancing, were terrible wine-imbibers, and addicted to the deep slumbers which follow heavy potations. They were no less dreaded by mortals than by the gentle woodland nymphs, who always avoided their coarse rough sports.
--Wineskin of the Satyr, water placed within becomes Dionysus' own vintage and imbues the drinker with appearance, personality, or qualities of a Satyr.
Priapus, the son of Dionysus and Aphrodite, was regarded as the god of fruitfulness, the protector of flocks, sheep, goats, bees, the fruit of the vine, and all garden produce. He bears in his hand a pruning knife, and his head is crowned with a wreath of vine and laurel. He usually carries fruit in his garments or a cornucopia in his hand, always, however, retaining his singularly revolting aspect.
--Set of Priapus, 3 sacred relics of his sect: Wreath of vine, Pruning Dagger, Cornucopia. Wreath worn as a circlet, can cast Grow Plant, Repel Vermin, Speak with Animals, etc. Pruning Dagger is magical, has effect on plant creatures: can be used to reduce CON to add bonus in other stat, incisions made can graft plants together to combine Special, Supernatural or Extraordinary qualities. Cornucopia casts Goodberry, Feast, Create Water etc. spells. Combination of the 3 relics enhance the power of each relic, but penalize the user CHA in all checks other than those made against plants & animals.
The SATYRS helped the OLYMPIANS in their war against the GIANTS. It is told that they came riding on asses, and when these beasts caught sight of the GIANTS, they were terrified letting out a braying such as the GIANTS had never heard, for which reason they took to flight and were defeated by the gods.
--Horn of the Ass; a shofar made from a horn gifted from the last tribe of unicorn, does sonic damage with bonus & fear effect vs. Giants.

"The Man and the Satyros (Satyr). A Man and a Satyros once drank together in token of a bond of alliance being formed between them. One very cold wintry day, as they talked, the Man put his fingers to his mouth and blew on them. When the Satyros asked the reason for this, he told him that he did it to warm his hands because they were so cold. Later on in the day they sat down to eat, and the food prepared was quite scalding. The Man raised one of the dishes a little towards his mouth and blew in it. When the Satyros again inquired the reason, he said that he did it to cool the meat, which was too hot. ‘I can no longer consider you as a friend,’ said the Satyros, ‘a fellow who with the same breath blows hot and cold.’"
Gorget of the Satyr; bearer may make breath attack in fire or cold flavor, but may not speak truth, penalty to diplomacy.
The triple-crested Korybantes (Corybantes) in their caverns invented this hide-stretched circlet [the tambourine], and blent its Bacchic revelry with the high-pitched, sweet-sounding breath of Phrygian flutes, and in Rhea's hands placed its resounding noise, to accompany the shouts of the Bakkhai (Bacchae), and from Mother Rhea frenzied Satyroi (Satyrs) obtained it and joined it to the choral dances of the Trieterides, in whom Dionysos takes delight . . .’
-- Retinue of the Rheans, instruments imbued with a compelling dance effect.
"Pan loved his neighbour Echo; Echo loved a frisking Satyr; and Satyr, he was head over ears for Lyde. As Echo was Pan's flame, so was Satyr Echo's, and Lyde master Satyr's. It was love reciprocal; for by just course, even as each of those hearts did scorn its lover, so was it also scorned being such a lover itself. To all such as be heartwhole be this lesson read: If you would be loved where you be loving, then love them that love you."
-- No idea this one, but who doesn't enjoy a love quadrangle?
"Honey was found by Bacchus [Dionysos], they say. He was leaving sandy Hebrus attended by Satyri, and had reached Rhodope and blooming Pangea; the hand-held cymbals of his companions clashed. Look, the ringing gathers strange aerial things, bees, who trail the sounds of the tinkling brass. Liber [Dionysos] collects the swarm, shuts it in a hollow tree and is rewarded by finding honey. When the Satyri (Satyrs) and the bald old man [Silenos] tasted it, they ransacked every grove for yellow combs . . . [Silenos is attacked by bees and] the Satyri come running and laugh at their father's bloated face; he limps from an injured knee."
--Cymbals of controlling Bees, instrument when played creates a flying Creeping Doom effect of stinging bees or a Vermin swarm. At end of spell, delicious honey fills the area making terrain difficult and slowing any who enter.
Finally, there are the gifts of the Faun in Pan's Labyrinth, but I don't understand the film enough to know whether they were boon or bane:
A book of tasks
3 magic stones to be fed to a toad
A mandrake root
Magic chalk
An hourglass
The aid of 3 Fairies
I suspect this was only barely helpful but I enjoyed putting it together.