The Imrei Yosher and HaRav Elyashiv shlita hold that pain is an intrinsic part of Bris Milah based on a Medrash regarding Avraham Avinu and general or local anesthetic may never be used during a bris. However, the Seridei Eish and HaRav Vozner shlita hold that it is not essential to feel pain and local anesthetic may be used, however general anesthetic should preferably be avoided because it is not acceptable to enter a covenant with Hashem while unconscious. The Maharsham and many other Poskim permit all forms of anesthesia, and this may certainly be relied upon under any extenuating circumstances. However, various forms of anesthesia have been known for centuries and it has never become accepted practice to use them during a bris, and one should not deviate from the established method without a valid reason.
It seems to me that an analgesic such as Tylenol, which reduces the intensity of the pain but does not eliminate it completely like an anesthetic would, should be acceptable even according to the most stringent opinion. It is interesting to point out that the Israeli Health Ministry only allows the use of a topical cream for pain relief during Bris Milah but not an injection.