The oldest extant maps of the battlefield are the so-called "Pigee map" and "Clove map" first published in Lawrence Babits' A Devil of a Whipping. These were evidently drawn not long after the battle, although by whom is unclear. My view is that these were not the work of a participant at the battle, but rather that they were produced by someone that had read (and wished to illustrate) the disposition of the British and American forces indicated by Morgan's after action report. Morgan's report mentions in one place that "The light infantry, commanded by Lieut. Col. Howard, and the Virginia militia under the command of Major Triplett, were formed on a rising ground, and extended a line in front." In another place it states that "Capts. Tate and Buchanan, with the Augusta riflemen, [were] to support the right of the line." Consistent with this description, the author(s) of the maps drew a battle line consisting of Howard's and Triplett's troops with another two companies forming a wing to the right rear consisting of Tate's and Buchanan's companies. This is exactly what someone relying solely on the report would have drawn; a participant would have known that Tate and Buchanan were part of Triplett's command, not a separate entity.
In any case, these maps have only recently come to light. The first battlefield map to be widely circulated was the map that William Johnson included in his 1822 Sketches of the Life and Correspondence of Nathanael Greene. I previously noted that the depiction is inaccurate, but it does have some strong points worth noting.
The Johnson Map (click to enlarge).
First of all, William Johnson clearly visited the battlefield. The three major elevations which I've previously described in connection with the battlefield are both present and correctly placed on his map.
Three Elevations on the Cowpens Battlefield.
Second, Johnson correctly placed the main American line between the first and second elevations on the battlefield. Although counterintuitive, this is indicated in various participant memoirs and pension applications (for a previous discussion, see: The Main Line: Location). For example, in one application, the son of North Carolina militiaman Thomas Lackey learned from his father "That at the Battle of the Cowpens the regulars were situated rather behind a hill."
Third, Johnson shows both troops of British dragoons attached to their front line charging the American militia, a point which most writers overlook, but which does seem indicated, on balance by participant accounts (see: British Cavalry Charges at Cowpens - Part 1, British Cavalry Charges at Cowpens - Part 2, Cowpens in Miniature 16, Cowpens in Miniature 18).
Fourth, Johnson shows that at the end of the battle, the British line had broken into two parts, which separately surrendered. This does not appear in Morgan's or Tarleton's description of the battle, but it is indicated in participant accounts (see: Cowpens in Miniature 21, Cowpens in Miniature 23). This further suggests that Johnson made an investment into learning what really happened at Cowpens rather than just rely on authority. This is clearly to his credit, even if he did err in some respects.
The chief problem, however, isn't the problems with Johnson's map, but it's rather with what was done with it. Henry Beebee Carrington printed a modified version of this map in his 1881 Battle Maps and Charts of the American Revolution.
For reasons not easily guessed at, Carrington turned Johnson's three elevations into two and he placed the Broad River on the edge of the battlefield, when in actuality it is miles away. Carrington's other deviations from Johnson were likewise unhelpful: he placed the main line on the crest of the foremost ridge and he reduced the number of charging troops of dragoons from two to one. Strangest of all, Carrington mistook the small rectangles representing the retreating American militia (lower right panel in Johnson's map) for British infantry units, and so has the British infantry drifting off to the right rather than directly advancing on the Continentals.
The Carrington Map (click to enlarge).
Although the Carrington map does not adhere well to the physical geography of the battlefield or participant accounts of the fighting, most of the subsequently-published battlefield maps adhere closely to the Carrington map. Notable exceptions can be found in the histories published by Edwin Bearss, Lawrence Babits, and John Moncure. All three of these distinguished writers prepared detailed maps based on multiple participant accounts and a careful consideration of battlefield topography. Two of these three works can be read in their entirety online, and Bearss' history is more than 40 years old. What does it say about the quality of contemporary treatments of the battle of Cowpens when Carrington should remain the gold standard and Bearss, Babits, and Moncure should have little discernable impact?
Lawrence Babits' 1998 A Devil of a Whipping: The Battle of Cowpens is available through amazon.com.
Will Graves transcribed the pension application of Thomas Lackey (.pdf file).
Henry Beebee Carrington's 1881 Battle Maps and Charts of the American Revolution.
Edwin Bearss' 1967 Battle of Cowpens: A Documented Narrative and Troop Movement Maps. (Also valuable is Edwin Bearss' 1974 Historic Grounds and Resource Study).
John Moncure published The Cowpens Staff Ride and Battlefield Tour.