I often wondered why a river god would be represented by a man-headed bull, or more precisely a man-faced bull. After purchasing this coin from Oiniadai I did a bit of research, and found the story very interesting.
In ancient Greek religion and mythology, Achelous (also Acheloos or Acheloios) was the god associated with the Achelous River, the largest river in Greece. According to Hesiod, he was the son of the Titans Oceanus and Tethys. He was also said to be the father of the Sirens, several nymphs, and other offspring. He was able to change his shape, and as a suitor for Deianeira, daughter of Oeneus, the king of Calydon, he transformed himself into a bull and fought Heracles for the right to marry Deianeira. Achelous was defeated, and Heracles married Deianeira. The story of Achelous, in the form of a bull, battling with Heracles for Deianeira, was apparently told as early as the 7th century BC, in a lost poem by the Greek poet Archilochus. According to a summary of a lost poem by the early 5th-century BC Greek poet Pindar, during the battle, Heracles broke off one of Achelous's bull-horns, and the river-god was able to get his horn back by trading it for a horn from Amalthea.
Sophocles, in his play Women of Trachis (c. 450-425 BC), has Deianeira tell her story, how Achelous wooed her in the shape of a bull, a snake, and a half-man/half-bull:
"For my suitor was a river-god, Achelous, who in three shapes was always asking me from my father - coming now as a bull in visible form, now as a serpent, sheeny and coiled, now ox-faced with human trunk, while from his thick-shaded beard wellheads of fountain-water sprayed. In the expectation that such a suitor would get me, I was always praying in my misery that I might die, before I should ever approach that marriage-bed. But at last, to my joy, the glorious son of Zeus and Alcmena came and closed with him in combat and delivered me."

Ancient Oiniadai lies on top of the Trikardo hills in the centre of the Acheloos River delta (NW Greece) at a distance of 9 km from the present coast. Its shipsheds testify to a former connection with the Ionian Sea. Because of its strategic position on the banks of the river Achelous with access to the Ionian Sea, the city of Oiniadai was a desirable possession for both the Akarnanian League as well as the Aitolian League. Its fortified walls, however, made it a difficult to acquire prize, and even the famed Athenian general Perikles failed to capture it when he led an army against it in 454 BC.
This series of bronze coins dates to the period when it was taken from the Aitolians by King Philip V of Macedon and restored to the Akarnanians. Production ended when the city was conquered by the Romans in 211 BC. Little is known of the history of Oiniadai after this, though it is known that it survived into at least the 1st century AD.

Akarnania - Oiniadai. Zeus / River-god Achelous. 219-211 BC.
Obverse: Laureate head of Zeus right. Reverse: Bearded head of man-headed bull, the river-god Achelous right, AP monogram behind. Reverse Inscription: OINIAΔAN above head. Bronze. Diameter: 22 mm. Weight: 6.1 gr.
Reference: BMC 6-7; BCD Akarnania 345