Yes, there was a "free produce" movement to encourage people to buy products made from free labor. Organizations like the Female Association for Promoting the Manufacture and Use of Free Cotton, the Free Produce Society of Pennsylvania, and the American Free Produce Association tried to encourage and facilitate these products. For example, in 1829, the Female Association for Promoting the Manufacture and Use of Free Cotton had just over 2,500 pounds of freely-produced cotton spun and made into various garments and bedding. The movement was, at the time, thought to be directly tied to the Quaker religion, but more recent scholarship shows that it was not solely Quakers who participated. Philadelphia was the stronghold of this movement, and by the 1850s the city had several free-produce shops.
However, there were challenges. Like cruelty-free products today, free-labor goods were typically more expensive. For example, when the American Free Produce Association attempted to acquire freely-made cotton from North Carolina, they found it difficult to competitively price the cotton because the local farmers found the work dangerous. Some supporters attempted to secure free labor production in Africa or the Caribbean and bring costs down, but these schemes never really took shape. Some also found the quality of free labor products poorer; Frances Ellen Watkins Harper noted upon buying a free produce dress that the cloth was rougher than cloth produced by slave labor. The movement never really took off en masse, and its supporters even struggled to convince other abolitionists or opponents of slavery to participate. A telling critique from one African-American abolitionist in the 1850s lamented that other free black Philadelphians would still choose to buy slave-produced goods.
Source: Faulkner, Carol. "The Root of the Evil: Free Produce and Radical Antislavery, 1820-1860. Journal of the Early Republic 27, no. 3 (Fall 2007): 377-405.
Edit for clarification: the contemporary lingo was "slave labor" or some variant like "unfree labor" for, well, enslaved labor, and "free labor" for work done by free people (not work done for free by slaves).
One example of this was advertisements for slavery free sugar substitute, or maple syrup, from the North. NY had a large amount of maple trees and Dutch Lutheran Gerrit Boone capitalized on this. in 1790, financed by the Holland Land Company, he bought 30,000 acres of trees to tap for syrup in the New York Adirondacks.
"It was hoped that Boon’s experiment would yield enough sugar to provide a generous return on his backer’s investment. His Dutch investors also hoped this new industry might compete with the sugar cane plantations in the south, and in so doing drive cane sugar from the market and deliver a blow against slavery. This may have been one of the first attempts at Socially Responsible Investing in the Colonies."
Because of the tremendous amount of sap required to make a gallon of syrup, it cost around $100,000 dollars in today's money to produce about 200 pounds of sugar in the first season of Boone's operation. The loss caused the Holland Land Company to pull out of the investment and end that early trial.
During the American Civil War, the Quakers thought that honey and maple syrup were moral alternatives to slave-produced white cane sugar. As such, honey and maple sugar became substitutes for cane sugar in many northern homes during the war. Keep in mind that the Northerners might not have had access anyway to cane sugar due to Confederate privateers blocking shipments from the Caribbean and other sugar producing areas.
Source from Adirondack historian Glenn Pearsall, Echoes in these Mountains (2008)
A similar question's been asked before. You may find some useful answers: https://www.reddit.com/r/AskHistorians/comments/1l86z3/before_the_american_civil_war_did_anyone_sell/