It is somewhat unlikely that tapeworms would cause the sort of persistent diarrhea that you are seeing but it is possible so it may be worth using a deworming medication for this parasite, too.
WebMD discusses diarrhea in cats including causes and treatments.
All cats have digestive troubles from time to time, and diarrhea is not uncommon. Usually, diarrhea lasts a day or so and clears up on its own. Other times, it may last for several days and cause dehydration, weight loss and lethargy. When your cat shows these signs, you'll most likely need to treat her with medication and reconsider her diet.
Diarrhea in Cats: Causes, Diagnosis and Treatment - Pet Education
Antibiotic medications can cause diarrhea, which may be the sign of a new infection. If your pet has diarrhea that is watery or has blood in it, contact your veterinarian. Do not use any medication to stop the diarrhea unless instructed by your veterinarian.
Learn the causes, diagnosis, and treatment of diarrhea in cats
Chronic diarrhea is typically a symptom of an intestinal disease that has disrupted the lining of a cat's intestines. Infections that can cause diarrhea may come from a parasite, bacteria, fungus or even a virus. A medication a cat may be taking could also cause diarrhea, as well as a food product a cat is allergic to or is toxic. Cancer, mal-absorption or mal-digestion disorders, inflammation of the bowels and diseases of major organs or systems of the body can also cause chronic diarrhea in cats. If we are going to use a trial and error approach I usually try metronidazole first but other vets like a different order. If it is successful I usually want to try sulfasalazine (Azulfidine Rx) when owners can readily give pills. If not, I might consider using injectable corticosteroids, usually methylprednisolone acetate (DepoMedrol Rx). In some cases, but not too often, we try to control the diarrhea using medications such as loperamide ( Immodium AD tm) or diphenoxylate (Lomotil Rx) for a few days.Chronic diarrhea is can negatively impact a cat's quality of life. With the proper diet and medication, a cat can enjoy the time in his home instead of loathing the time in the litter box. Many medications that we dispense to your pet can cause diarrhea. Thyroid medication, NSAI drugs such as Rimadyl and aspirin, worming medications, and topical insecticides are only a few of the many medications that can cause diarrhea. Some pets are just sensitive to a particular medication. Some pets do better when less of the medication is given or when less is given - but in more frequent doses.