You talk about black operations, which Wikipedia defines as:
A black operation (or black op) is a covert or clandestine operation by a government agency, a military unit or a paramilitary organization; it can include activities by private companies or groups. Key features of a black operation are that it is secret and it is not attributable to the organization carrying it out.
It goes on to talk about black bag operations, which are an activity within a black operation. Again, from Wikipedia:
A single such activity may be called a black bag operation; that term is primarily used for covert or clandestine surreptitious entries into structures to obtain information for human intelligence operations.
Such black bag operations are also carried out by the FBI. For example, this ABC article from 2007 states:
"The refocusing of FBI operational priorities and the new emphasis placed on intelligence-based activities…has resulted in a dramatic increase" in the demand for so-called "black bag" jobs, in which teams of highly-trained specialists covertly enter a home or office, search its contents and leave without indicating they had been there, states the budget document. It does not detail how many of the secret searches it carries out, and the FBI did not respond to comment. The bureau is asking Congress for an additional $5 million to pay for the operations and more than a dozen new specialized personnel.
In 1995, most of the FBI’s secret search operations were related to criminal investigations, according to the document. Last year, close to 90 percent of such operations were for national security matters, it asserts.
An example of such an operation by the FBI on US soil is described on Wikipedia:
As example, in 1947, after American spy Elizabeth Bentley had defected from the Soviet underground and had started talking to the FBI, the FBI broke into her Brooklyn hotel to do a "black-bag job" to verify her own background – and to look for anything otherwise. "They found nothing out of the ordinary."
The FBI also lists a number of documents regarding older such operations on its website.
So the answer is no, the FBI handles such operations as well that we know of. There may also be other organisations that coordinate such operations, but the FBI examples suffice to answer the question and I haven't been able to find explicit references of other organisations or agencies (in the US).