The Constitution has been amended only 27 times in its 220-year history. Even that number arguably overstates the case. If we consider the Bill of Rights to be one action of amending the Constitution, rather than 10 separate amendments, that reduces the number to 18. The same can be said of the "Civil War Amendments", the 13th, 14th, and 15th amendments, which freed the slaves, and gave them (in theory at least) civil and political rights. If we look at it that way, the Constitution has been successfully amended only 16 times.
One example of a constitutional amendment that was ratified to reverse a Supreme Court decision, is what is probably the least popular of the amendments currently in force. That is the 16th Amendment, which allows the federal government to levy an income tax. (Its main rival in unpopularity, the 18th Amendment, which prohibited alcoholic beverages, has, of course, long since been repealed.)
A federal income tax was implemented in 1861, to help cover the cost of the Civil War. That tax eventually expired, but Congress imposed another income tax in 1894. The Supreme Court ruled that tax unconstitutional, the following year.
The Constitution grants Congress the power to levy taxes. But it also provides that "direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers", i.e., their populations, as determined by the decennial census.
In the 1895 case of Pollock v. Farmers' Loan & Trust Company, the Supreme Court found that, to some extent at least, the income tax constituted a "direct tax", and therefore, because it was not apportioned among the states according to population, it violated the constitutional provision quoted above.
The 16th Amendment got around the direct v. indirect question, as follows:
The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.
The amendment was submitted to the states by Congress, in 1909. The ratification process was completed on February 3, 1913, 29 days before Woodrow Wilson took office as president. Wilson signed a new income tax bill in October of that year, and the tax that we all know and love has been with us ever since.
Other such efforts to amend the constitution have failed.
The 1962 Supreme Court decision in the case of Engel v. Vitale, disallowed a prayer that a public school district required to be recited in schools. A majority of the justices found that it violated the following provision of the First Amendment:
Congress shall make no law respecting an establishment of religion ...
The decision set off a firestorm of controversy, as did several additional school prayer cases that subsequently came before the Court. That led to several proposals for constitutional amendments, along the lines of:
Nothing in this Constitution, including any amendment to this Constitution, shall be construed to prohibit voluntary prayer or require prayer in a public school, or to prohibit voluntary prayer or require prayer at a public school extracurricular activity.
None of those proposals has made its way through the Congress, let alone been ratified by the states.
Proposed constitutional amendments to overturn the Court's 1973 decision in the case of Roe v. Wade, which severely restricted states' leeway to prohibit abortions, met with a similar fate.