I'm not sure about any attempts in the 19th century, but George Washington and Thomas Jefferson both tried to acquire buffalo in the late 18th century, with Washington specifically wanting the animals for the purpose of pulling plows. Washington may have gotten the idea from a contemporary newspaper report of a man who claimed to have successfully used a buffalo for this purpose.

Unfortunately for Washington and Jefferson, buffalo were all but extinct east of the Appalachian Mountains by the time the U.S. gained its independence, so they had to commission hunters traveling to the Ohio Valley to procure the animals. Washington sent at least two men out with this purpose and Jefferson one.

These attempts all failed for a number of reasons but a big problem for those seeking buffalo at this time was that there was no way to bring the animals back east alive. Obviously there were no trains or cars back then to ship the animals, and rivers generally don't flow up mountains, so most water travel routes were out of the question. The hunters couldn't herd the animals because buffalo don't take to herding the same way that cows do. They overheat quickly and scare easily. Because of this, if you try to drive a buffalo, it will often die of heat exhaustion, attack the drivers' horses, or injury or kill itself trying to get away.

There are ways to get around this. For example, one person in 18th century Spanish Texas who wanted a buffalo came up with the idea of capturing infant buffalo and using a nursing cow to draw them back to civilization. Another solution to herders in Texas was to drive a whole herd of buffalo realizing that while most of them would die before they reached their destination, a few would survive. It is unlikely that the hunters hired by Jefferson and Washington were aware of these solutions.

In spite of this, Washington may have been successful in acquiring a pair of the animals, as an account of his estate at his death lists two "buffaloe." Unfortunately, I've been unable to find how Washington came into possession of these animals or anything else about them. Because of this, it is possible that the animals were water buffalo, not American bison. From what I'm able to tell, the closest Jefferson got to having a buffalo was a stuffed buffalo head he received as a gift from Lewis and Clark.