The US was responsible for Diem's assassination in only a very small way.
The major way in which the US was responsible was in the fact that it did not try to stop the coup from occurring. In fact, Ambassador Lodge told the coup plotters that the US would not oppose a change of leadership in South Vietnam.
However, this does not mean that the US was responsible for the coup, much less the assassination. The US did not commit the blunders that made Diem so unpopular. The US did not gather the generals and propose the coup. Above all, even if the US wanted Diem replaced, they had no reason to want him killed.
The US permitted the coup and even encouraged it. To some small extent, that makes the US partially responsible for its outcome. But overall, the major responsibility for the coup and especially for Diem's death belongs to Diem and the people who planned and carried out the coup.