TL;DR: Those "Wild West" Posters didn't have real equivalents in the Golden Age of Piracy, just a couple text-only proclamations because period circumstances would make it close to impossible to pull off a "Wild West" style poster with picture and everything.

Long explanation:

I only know of one thing that could be considered a "wanted" poster. There was a 1696 proclamation for the pirate Henry Every for his arrest and offering a £500 reward. It doesn't look anything like the traditional wanted posters that most are familiar with from the 19th century (especially the "wild west" stuff). Here is a more readable copy of the Proclamation and here is an original on display in the St. Augustine Pirate & Treasure Museum.

I'm guessing I'll get these two questions sooner or later, so I'll answer them now:

1. How come they don't have a picture or detailed descriptions on the poster/proclamation?
   Among the period documents I've seen relating to pirates in the 1690 to 1725 period, descriptions of pirates are limited. There have been some, such as a quick sentence in the period Boston Newsletter describing Blackbeard (or Edward Thatch) as a "tall spare man with a very black beard which he wore very long" or pirate captain Paulsgrave Williams' (often sailed under or in consort with Samuel Bellamy) described in a deposition of John Lucas, Master of the Ship Tryal on April 13, 1717 as, "a middlesized man of a dark brown complexion wearing a peruke." But, these descriptions are short and few in number. Nothing enough to provide a good image anyway and even then, that doesn't equate to something that would be good enough for an identifiable picture. The images of pirates that are even close to being made during the Golden Age of Piracy are all created from the imaginations of artists who never saw them in real life. Then there's the whole business of the limitations of period printings providing a realistic enough reproduction of such a image for identification. So beyond not having evidence that such an image was ever made of a pirate from real life encounters for a wanted poster, the ability to do it wouldn't really be there to do it either.

2. How come more Proclamations weren't put out like this and why did Every get one?
   Pirates played havoc to trade and order in the greater Atlantic world and in the Indian Ocean from time to time - it's true. Plenty of period newspapers had descriptions of attacks by pirate attacks that took place. You only sent out proclamations when there was a threat that required such a proclamation. The pirates individually during the Golden Age of Piracy didn't need proclamations (especially when it could be hard at times to trace which ones were doing what), but they did get one collectively in 1717. Not only did this "A PROCLAMATION for Suppressing of PYRATES" from Hampton Court on September 5, 1717 offer a pardon to pirates that surrendered themselves (that's a generalization, but besides the point), they also offered blanket rewards to capturing/taking pirates that didn't surrender themselves. It read as following:

And we do hereby further declare, that in Case any Person or Persons, on, or after, the 6th Day of September, 1718, shall discover or seize, or cause or procure to be discovered or seized, any one or more of the said Pyrates,...shall have and receive as a Reward for the same, viz. for every Commander of any pirate Ship or Vessel, the Sum of £100[,] for every Lieutenant, Master, Boatswain, Carpenter, and Gunner, the sum of £40[,] for every inferior Officer, the Sum of £30[,] and for every private Man, the Sum of £20.

So with this proclamation, it basically did what one of your "wanted posters" would but without needing specific information to each individual pirate and addressed the greater threat from all the pirates. Also, if you're wondering why individual warrants weren't issued, don't forget this is before the U.S. and before the whole "innocent until proven guilty" era. Courts ran a bit differently back then.
Henry Every, meanwhile, was from a period before that proclamation. First, he and his English comrades who had been recruited (questionable term, but besides the point) to man ships for the Spanish mutinied and took a sizable ship of force (the Spanish were allies to England at the time in the Nine Years War, or the War of The Grand Alliance). Also his actions resulted in some political issues with England's trade partners in India. Every attacked and captured rich vessels from the Great Mogul in way to pilgrimage to Mecca. Large amounts of wealth were taken and atrocities enacted upon the passengers. But, they were English pirates, and the people from India did not see much difference between the pirates and the English authorities themselves, and held the English responsible for the pirates. This trade between India and England held a significant position in the English economy, so it took a high priority for the government to hunt down and prosecute to show that they wouldn't tolerate such actions. Similar issues happened with the privateer turned pirate William Kidd (and I can't remember/find if a similar proclamation went out with such a reward for him).
For more information on Henry Every and/or Captain Kidd, I recommend E.T. Fox's King of the Pirates: The Swashbuckling Life of Henry Every (though, good luck getting that book these days) and Robert C. Ritchie's Captain Kidd and the War against the Pirates (it's a better and more scholarly book than Mr. Zack's book The Pirate Hunter)

Oh, and if you are still going to make your board game and want to make stuff look period, including the font, this should be a help, someone went back to the old newspapers of the 17th century and 18th century and made fonts based on the old type (they are really spot on): http://iginomarini.com/fell/the-revival-fonts/