Can you shoot an animal with a tranquilizer, or feed a tranquilizer to an animal, and proceed to slaughter it in a kosher manner?
Generally the answer is no. This came up in the 1930s in Germany, where the laws were demanding that animals be stunned before slaughter. Rabbi Yechiel Yaakov Weinberg wrote on the subject at length and corresponded with many great authorities, but at the end of the day Rabbi Chaim Ozer Grozinski put his foot down that the practical answer was "no."
Rabbi Weinberg's work of responsa, Sridei Aish, has a lengthy addendum containing his correspondence on the subject.
One concern is the stunning/tranquilizing may injure the animal, and we require that the animal be in good shape just before slaughter. Another is that we want maximum bleed-out just after slaughter, which is accomplished when the animal has a fully-functioning nervous system.
what will stop you (what is the possible transgression?),
but if you want to eat it the possible problems are,
the chemicals that you put in the animal are not healthy (i heard it is recommended to wait a few days for them to leave the body), i found on google
when you shoot it with a needle you need to be careful not to puncture the organs which become traif from a hole, i.e. esophagus, lungs, stomach, gallbladder, part of the spleen, intestines, uterus (shach, yora daiya, 29.3)