First and foremost, I would find a new pediatrician. I personally dont think 2 month old babies have the mental capacity to have "tantrums" as they really are just aiming to have their needs met.
Did your doctor do anything to look into possible acid reflux? One of my twins was diagnosed with it around 6-8 weeks. He also had a milk allergy so we put him on Nutramigen rather than a milk based formula. For the reflux, he was put on Zantac and Reglan (one to help neutralize and one to help keep it from creeping up) and the combination made a HUGE difference. He went from being a baby who screamed and arched his back and was just inconsolable to actually enjoying life. Before the meds, looking at pictures of him, you can see this totally stressed and strained look in his eyes, poor guy! WE also kept him upright most of the time, as laying on his back would often exasperate the problem. So, for about six months he slept in his swing (the pediatrician said it was fine, if it works then do it :)
I definately would NOT accept "tantrums" as the answer. Who is your current ped? If you are in the heights, Dr Kim-Hoffman (Pres) at Northside Pediactrics is fabulous and very proactive at getting to the bottom of things. SHe was our doctor until we moved to Rio Rancho. If you are on the west side, Dr Syvia Crago (Pres) is amazing! We currently go to her and she is just fabulous, I can't imagine life without her :) I also have heard that Dr Good (Lovelace) in Rio Rancho is very very good. I have a few friends who go to him and he is great from what they say. But more importantly, my experiences with the two from Pres and my friends with Dr Good, we have ALWAYS felt like the doctors KNOW that we KNOW our babies/kids well enough to know that something is not right. You have two older kids, you would know if it is a baby who wants to be held and a baby who has something that needs to be fixed/changed. If your gutt is telling you that something needs to be fixed/changed then find a doctor who will take that and run with it. A mothers intuition is to be trusted more than a doctor who wants to get on to the next patient.
Sorry to ramble, your doctors answer just got my in the rambling mood I guess :)