What programs or laws did President Kennedy and President Johnson instill in order to combat civil rights violations? In your opinion, what was the most successful civil rights law?

Because Kennedy had limited Congressional support and a short presidency, his Civil Rights legacy centers more around combating violations rather than enacting new legislation. One of Kennedy’s first actions involved integrating Ole Miss in 1961, when the Mississippi governor tried to prevent Meredith from enrolling at the university. JFK intervened and ordered the national guard to escort Meredith onto campus, where he was still met with protests and violence. The Freedom Rides of 1961 also presented a challenge to Kennedy’s presidency. Students and civil rights workers, white and black, rode throughout the South in order to register black people to vote. Because of the violence they faced, Kennedy urged the Interstate Commerce Commission to desegregate interstate travel (travel between states). Kennedy was also successful in getting an Equal Pay Act passed in 1963, which banned unequal pay based on sex.
Unfortunately, while JFK personally supported civil rights, he was also looking ahead to the Election of 1964 and worried about pushing civil rights legislation to the point of losing the support of the Democratic Party, especially southern Democrats. He therefore delayed sending a civil rights bill to Congress at first. However, when Alabama Governor George Wallace refused to integrate the University of Alabama, and then when civil rights leader Medgar Evers was killed in Mississippi in 1963, JFK drafted and sent a civil rights bill to Congress. This bill, which would become the Civil Rights Act of 1964, called for an end to discrimination in employment, segregation in public places, and discrimination in voting (especially literacy tests in the South that prevented many black people and poor white people from voting). Kennedy was assassinated in 1963, while Congress was still heavily debating the bill.
When President Johnson came into office, he appealed to Congress to pass Kennedy’s civil rights bill in memory of the slain president. Johnson’s lobbying efforts were successful, and in July LBJ signed the Civil Rights Act of 1964. Included in the law were the following provisions:

prohibited discrimination in public places


mandated the integration of schools and other public facilities


made employment discrimination illegal.

The 24th Amendment was also ratified in 1964, making poll taxes illegal. Then in 1965, Johnson signed the Voting Rights Act, which is perhaps one of the most significant pieces of civil rights legislation. In 1965, MLK and other civil rights leaders and groups organized a peaceful protest from Montgomery to Selma, Alabama to protest voting discrimination that persisted despite passage of the Civil Rights Act of 1964. State troopers brutally attacked the protesters, gaining national media attention and leading LBJ to call for voting reform. The Voting Rights Act banned the use of literacy tests and gave the federal government the ability to investigate discriminatory voting practices.
Finally, LBJ also used his Great Society legislation to attempt to reduce social and racial inequality. From 1964-1967, over 200 pieces of legislation were passed as part of Johnson’s Great Society, which addressed inequality and issues in education, poverty, and the environment. It included programs like Medicare and Medicaid, Food Stamps (SNAP), Job Corps, the Department of Housing and Urban Development, and federal loans and grants for education. While the Great Society had mixed success in alleviating poverty and ending discrimination, the poverty rate declined significantly and racial gaps in education and income began closing. Overall, LBJ’s Great Society and civil rights legislation are seen as having mixed results, in some ways leading to greater equality (especially in voting and ending segregation), while also falling short of its more lofty goals (like reinvigorating the cities and closing racial wealth gaps).
https://millercenter.org/president