Since the definition of a protest usually assumes a disruptive mass demonstration, it might be hard to find examples of the kind that are pro-government. There are plenty that might be considered reactionary, and still more in which the point is to further solidify a racial, social, or class power structure that previously existed. Pogroms, or massacres that target ethnic minorities, are often either initiated by or tolerated by local governments (or at least their officials), and might fit what you're looking for.

I can give a better, deeper example about a protest that was openly pro-government that took place early in the War of 1812. Generally called the Baltimore Riots, they took place over the course of more than a month over the course of June and July, 1812. Though started as a spontaneous - if highly organized - act of political violence aimed at the printing offices of an anti-war newspaper, the Federal-Republican, the violence soon turned more general, more widespread, and involved targeting perceived enemies of the Madison administration, opponents of the war, and racial minorities.

That it took place in Baltimore should be no surprise. Baltimore was a rambunctious town that was known early in its existence as "mobtown" for the frequent eruptions of political violence that occurred there. In June, 1812, the conflict was about the war, which was deeply unpopular, especially among the country's Federalist party, the party in opposition to James Madison's Democratic-Republican party. To be short, the Federalists opposed the war for a variety of political, moral, religious, and financial reasons, and not every Federalist agreed with every other; it was a fractious party that had old roots, and the only thing holding it together ideologically in 1812 was its opposition to Madison.

Madison's Democratic-Republicans, on the other hand, supported the war mostly as a means of protecting American dignity and sovereignty, expanding its borders, and protecting its trade fleet. A series of efforts in the lead-up to the war had only deepened the conflict between the two parties, as Jefferson's harsh restrictive acts had done little but harm American trade at the expense, mostly, of his political enemies: northern merchants, bankers, insurance agents and early industrialists.

Politics of the time were nakedly acerbic and provocative. Thomas Jefferson's 1800 campaign infamously called Adams "hermaphroditical," for instance, and public mud-slinging was more or less expected of the press.

In any case, the Federal Republican was based in Baltimore and was an unrepentantly Federalist paper, loudly and forcefully denouncing the war and the Madison administration. Men of Baltimore who supported the war took offense, and on the night of June 22nd a crowd gathered outside the printing office and destroyed it, pulling the building down and destroying its press.

The crowd did not stop once the Federal-Republican office was destroyed. Night after night, mobs gathered in Baltimore and continued its riotous conduct, targeting most of its ire against individuals who had spoken out against the war. Though ships, homes and businesses of publicly Federalist or anti-war individuals were the initial targets, the riots soon began illuminating other social tensions as well. Two homes owned by a free Black, James Briscoe, were destroyed, even after the mob had to break in and drag Briscoe's daughter out of her house. Afterward, the mob went on to target the local African church. The riots continued from June into late July.

Alexander Hanson, one of the owners of the Federal-Republican, came back to Baltimore to personally oversee the reestablishment of the paper. Other mobs in other cities drove out Federalist newspapers, such as the Savannah, Georgia, American Patriot. In Connecticut, a bastion of Federalist support, the Courant wrote that the war's cause was pretense, and instead "is valiantly waged against the freedom of the press." Baltimore's mayor, Edward Johnson, himself an outspoken Jeffersonian, had half-heartedly failed to stop the riots on the first night, but was dismissed by the mob. "Mr. Johnson," the mob's spokesman entreated the mayor, "that house is a temple of Infamy, it is supported with English gold, and it must and shall come down to the ground." Hanson felt justified in not only resuming printing of the Federal-Republican but bringing along 50 armed supporters to protect the place.

Hanson returned to Baltimore in July, and began printing again with the new address of the paper in full display on the page. The next day, another mob formed almost immediately, and refused to disperse even after the defenders of "Fort Hanson" fired a blank volley out the windows, a group of men stormed the place. The Federalists inside fired live ammunition to defend themselves, and killed Thadeus Gale, a local doctor, who had led the charge. Eventually surrendering to the local militia for protection from the increasingly large and violent mob, the new location of the Federal-Republican was destroyed. It did not end there. Ascertaining the location of the "tories" (a pejorative term that had been used against loyalists during the American Revolution and had been resurrected for common use against Federalists), the mob stormed the jailhouse and captured Hanson, Revolutionary War generals Light Horse Harry Lee and James Maccuban Lingan, and several others, and dragged them out into the street to beat them savagely. Hanson and Lee were badly injured, and Lingan was killed by men wielding a variety of weapons: clubs, bricks and fists were liberally used, and candle wax was even poured into their eyes and on their faces. Lee and Hanson never recovered fully from the injuries inflicted upon them, and both died before the decade was out.

The riots had started on June 22nd and had not stopped between then and July 28th, when they destroyed the second Federal-Republican office. In between, the riot had raged throughout the town, targetting Federalists, free blacks, Irish people, laborers, and others. It was unambiguously a pro-government, pro-war force, using violence to suppress voices of opposition and targets of social and racial ire.

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There's a brief account of the riots, written from the Federalist side, that was published in September, 1812, which you can read here.

I'd also recommend Adam Malka's The Men of Mobtown as a broader examination of political violence in Baltimore, though the period post-dates 1812, for the most part.

Much of the detail of the riots is in Paul Giljie's "The Baltimore Riots and the Breakdown of the Anglo-American Mob Tradition"