If he's eating and drinking normally and acting himself, I would start with taking a fresh stool sample to your vet. The fresher the better, but most tests can be effectively run on samples as old as 12 hours. Also, an abnormal stool (the nastier the better) is more likely to show parasites or bacteria than a more normal looking stool.
I don't know what deworming tablets you are using, but there is no oral medication in the world that stays in the body for 3-6 months. The tablets you are using may recommend re-dosing them every 3-6 months, but the medication itself is gone within 24-48 hours. Also, there is no single deworming medication on the market that will treat all of the intestinal parasites that your dog may be exposed to. So, even if you are deworming him on a regular schedule it is still very possible for him to have picked up worms and for that to be the cause of the diarrhea. The fact that you have a new dog in the home makes parasites even more likely as she could have brought them home with her.
Carrots and tomatoes are unlikely to cause diarrhea if he is eating them regularly. And they won't cause an obstruction. Tennis balls and clothes pegs however could cause an intestinal obstruction! If he's vomiting, not eating well, and/or lethargic and you suspect you are missing something along the lines of a tennis ball then he needs to see the vet right away as an obstruction is deadly if not treated.
