Toddler's Diarrhea: This is a common condition in toddlers characterized by chronic, non-bloody diarrhea, often without other symptoms. The child's age, duration of diarrhea, and absence of other symptoms such as fever, abdominal pain, or vomiting make this a likely diagnosis. The fact that the child is eating, drinking, and urinating normally also supports this diagnosis.

Viral Gastroenteritis: Although the child does not have vomiting or fever, some viral infections can cause prolonged diarrhea without these symptoms. The child's ability to eat and drink suggests a mild infection.
Food Intolerance: Lactose intolerance or intolerance to other dietary components could cause chronic diarrhea in a toddler. The absence of other symptoms and the child's normal appetite and urination pattern could be consistent with this diagnosis.
Functional Diarrhea: This condition is similar to toddler's diarrhea but can be seen in children of various ages. It is characterized by chronic diarrhea without an identifiable cause, and the child otherwise appears well.

Inflammatory Bowel Disease (IBD): Although less common in this age group, conditions like Crohn's disease or ulcerative colitis can present with chronic diarrhea. The absence of blood in the stool, fever, or abdominal pain does not rule out IBD, as these symptoms can be intermittent or mild.
Intussusception: This condition, where a part of the intestine telescopes into another, can cause intermittent abdominal pain and diarrhea. Although the child does not have abdominal pain, intussusception can sometimes present atypically, especially in young children.
Malabsorptive Disorders: Conditions such as celiac disease can cause chronic diarrhea due to malabsorption. The child's normal appetite and absence of weight loss do not rule out these conditions, as they can have a gradual onset.

Chronic Infections: Certain infections like giardiasis can cause prolonged diarrhea in children. These are less common but should be considered, especially if the child has been exposed to untreated water or has traveled to areas where such infections are common.
Congenital Anomalies of the Gut: Although typically diagnosed earlier in life, some congenital anomalies can present with chronic diarrhea in toddlers if they were not symptomatic at birth or if the symptoms were mild.
Immunodeficiency: Children with immunodeficiencies can be prone to chronic or recurrent infections, including those causing diarrhea. The absence of other infections or symptoms does not entirely rule out immunodeficiency, but it makes it less likely.