Gastroenteritis: This is a common cause of yellow liquid stool, and it can be triggered by a variety of factors including viral or bacterial infections. The frequency of two times a day could be consistent with a mild to moderate case of gastroenteritis.

Cows Milk Protein Allergy (CMPA): As mentioned in the question, an allergy to cow's milk protein could lead to gastrointestinal symptoms including diarrhea, which might present as yellow liquid stool. This is particularly common in infants and young children.
Lactose Intolerance: This condition, where the body is unable to digest lactose due to a deficiency of the enzyme lactase, can lead to diarrhea and potentially yellow liquid stool after consuming lactose-containing products.
Irritable Bowel Syndrome (IBS): Although IBS can cause a variety of bowel symptoms, including diarrhea, it's less likely to cause solely yellow liquid stool. However, it remains a possibility, especially if other symptoms like abdominal pain or bloating are present.

Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can cause chronic diarrhea, which might occasionally appear as yellow liquid stool. These conditions can have serious complications if not diagnosed and treated properly.
Giardiasis: An infection caused by the Giardia parasite, which can lead to chronic diarrhea. It's crucial to diagnose and treat this condition to prevent malabsorption and other complications.
Celiac Disease: An autoimmune reaction to gluten can cause malabsorption and lead to diarrhea. While celiac disease is more commonly associated with malabsorptive symptoms, it's a condition that should not be missed due to its potential for long-term complications.

Bile Salt Diarrhea: A condition where there's an excess of bile salts entering the colon, which can cause diarrhea. This could potentially result in yellow liquid stool due to the bile content.
Short Bowel Syndrome: A condition that results from a significant loss of intestinal tissue, leading to malabsorption. Diarrhea can be a symptom, and in some cases, it might appear as yellow liquid stool due to the rapid transit of intestinal contents.
Whipple's Disease: A rare, systemic bacterial infection that can cause malabsorption and diarrhea among other symptoms. It's extremely rare but important to consider in cases where common diagnoses have been ruled out.