Congress can change or outlaw any punishment for any law it enacts.
In fact, Congress has stricken several forms of corporal punishment already by statute, which had been all common when the constitution was adopted.
The process is to simply remove the relevant article that allows a punishment from the statutes. Judical Corporal Punishment - flogging - had been deemed appropriate by the founding fathers: Washington requested to be allowed to flog soldiers 500 times because the next step after 100 was putting them to death and Jefferson had proposed to castrate rapists. In fact, better read all of Thomas Jefferson: *A Bill for Proportioning Crimes and Punishments (1778) - the guy had some ideas that nowadays are seen very cruel and unusual, among them death by hanging and poisoning poisoners.
It's attested that both Lincoln and Roosevelt did advocate to flog men who beat their wives, and Georgia had flogging in the early 1950s. But do we find that punishment in the books still? No, it has been stricken from the books, piece by piece: Delaware used to have it quite long. A 1964 NYT article describes that flogging seems to be "at an end":
It now seems probable that, like the pillory, which went out of style here [Delaware] in 1905, the whipping post will be banished by the courts before further sentences can be carried out.
The legislative mood [in support of flogging] was reflected in 1961 when the General Assembly voted to repeal its own 1958 law abolishing capital punishment [including flogging], and then overrode Gov. Elbert N. Carvel's veto of the reinstatement measure.
However, it took till 1972 to actually get whipping abolished, as Delaware Times reports by replacing large swaths of the criminal code:
The 1971-72 legislature saw the birth of the Coastal Zone Act and the death after 350-plus years of the Delaware whipping post.
One major accomplishment of the 1972 second session stands firm: a new criminal code for Delaware. It’s almost exactly 45 years since Peterson signed the code into law at Buena Vista at 9 a. m. July 1, 1972. The code became effective a year later and meant the end of Delaware’s infamous whipping post.