Gastrointestinal bleeding: This is the most likely diagnosis, as NSAIDs are known to cause gastric mucosal damage and bleeding, leading to black, tarry stools (melena). The mechanism involves the inhibition of prostaglandin synthesis, which normally protects the gastric mucosa.

Iron supplements: Iron supplements can cause black stools due to the oxidation of iron. Although this is not directly related to NSAIDs, patients taking NSAIDs might also be taking iron supplements for unrelated reasons.
Bismuth-containing medications: Bismuth, found in some medications like Pepto-Bismol, can turn stools black due to its sulfide-producing properties. Patients might be taking these medications concurrently with NSAIDs for gastrointestinal protection or other reasons.
Upper gastrointestinal malignancy: Although less common, upper GI malignancies can cause bleeding, leading to black stools. The use of NSAIDs might exacerbate symptoms or be coincidental.

Peptic ulcer disease: This is a critical diagnosis not to miss, as NSAID-induced peptic ulcers can lead to severe, life-threatening bleeding. The presence of black stools could be an indicator of such a condition.
Gastric ulcer with perforation: Although less likely to present initially with black stools, a perforated gastric ulcer is a medical emergency that requires immediate attention. NSAID use increases the risk of such complications.
Esophageal varices: In patients with liver disease, NSAIDs can increase the risk of bleeding from esophageal varices, which can present with hematemesis or melena.

Ingested black licorice or other substances: Certain foods or substances can temporarily turn stools black. While not directly related to NSAIDs, it's a differential to consider in the absence of other symptoms.
Intestinal ischemia or infarction: Although rare, intestinal ischemia can cause bleeding, leading to black stools. NSAIDs might be used in patients with conditions that increase the risk of intestinal ischemia, such as cardiovascular disease.