In a separate question, it was suggested that because Jews tend not to proselytize, there would not, in contrast to slaves who became Christians, be many Blacks who became Jewish even though their owners followed that religion. But has there been any records of this ever happening?
There seem to be two parts to your question: did slaves owned by Jewish masters ever adopt the Jewish religion, and has it happened in recent years that African slaves owned by North American Jews became Jewish.
The answer to the first part of your question is an unequivocal yes. A close reading of the Pentateuch's slave regulations would suggest two different types of slaves: Jewish and "Canaanite". Jewish slaves are effectively indentured servants. They worked for the length of time that it takes to pay off a debt or make good on theft, and either go free automatically at the end of seven years or with the arrival of the jubilee year (the fiftieth year of the fifty-year agricultural cycle) - whichever comes first.
Canaanite slaves, on the other hand, were property. When their owner died, they were inherited along with the rest of his property, and only went free if they were deliberately released. It's pretty ugly, but was very much a reality of the time (in fact, it was only relatively recently in Jewish history that people stopped thinking of slavery as a natural human condition - around the same time that people stopped thinking of it this way in general human society).
I mention all this because it is a clear precept of the early rabbinic literature that non-Jewish slaves ("Canaanite slaves") who are owned by Jews are to be considered Jewish to the extent that they are partially bound by Jewish law (such slaves are often classed together with women and minors in this regard) and that if they go free they are to be considered entirely Jewish, and are entirely bound by Jewish law. Where the early rabbinic literature speaks of freed slaves, it is referring to people who were not Jewish by birth, since Jews cannot be owned by Jews and remain fully bound by Jewish law even as indentured servants.
In more recent years, there were some cases of Jewish slave ownership in North America, but assessing its prevalence is complicated. Jews were primarily concentrated in the north of the country, and their voices feature prominently amongst abolitionists, but there were at least some southern slave owners who were Jewish. This Wikipedia article contains some good information, as does this review of a rather controversial book.
As to the number of former slaves who became Jewish after their emancipation, I do not know of any studies. Somewhat anecdotally, there are some African American Jews with Hebrew surnames or with Ashkenazi customs, who can trace their Jewish heritage back to the 19th century. Whether or not this is because their ancestors had been "owned" by Jews (as deplorable as that verb sounds), I do not know.