agree second opinion due to age i would have them do a fecal weekly for 3-4 weeks so just take on in once a week and have it tested for giardia and coccidia as those tend to run in puppies and giardia is very hard to detect. They should give either metronidazole or tylan powder to clear it up - watch for dehydration if small as diarhea is more dehydrating than vomitting. Cook up some white rice as that is binding and also get a 1/4 tsp of organic pumpkin and mix that together along with probiotics dds plus from vitamin shoppe and see if he will lick 2 capsules of probiotic off plate 30 min before food in am then mix in the pumpkin and rice with food so cut back a little on the kibble. This should help and more natural but if a parasite like giardia make sure to clean his butt everytime and clean the area real well as they can keep reinfecting themselves
info on both
Giardia canis in Dogs Coccidia (Coccidiosis) in Dogs: A Cause of Diarrhea
did you switch foods recently as that can cause diarhea as well if food is too rich