Let us suppose that during the 1820s to 1830s, men of good intent come together in the United States and bring about a peaceful agreed solution to the slavery issue that sees slavery ending in a way that both North and South can accept.
As a result, there is no American Civil War. So, what are the effects inside the United States and elsewhere?
It's an interesting WI, but to truly asses the consequence we'd need to be more specific on how slavery ends. IMO, the most likely sources is a successful adoption of the Floyd plan in the 1830s (Gabriel Prosser's Rebellion is never launched). This anti-slavery movement would be native to the south, not connected to the issue of states' rights. It would also be heavily connected to a move in industrialize the South. I can't remember though what they proposed to do with the freed slaves (a big question, though). You might also have a different scheme, one that focused on compensating slave owners; this might be effective if the slave owners received Treasury bonds managed by a renewed Bank of the United States. Such a move betokens a big change for the Southern Planters' typical fear of Banks, however. Making the movement in any way a national one has the potential to create resistance in the South.
The first question is what happens to the politics of Western Expansion. The Floyd Plan POD isn't enough, IMO, to stop the dynamics of the Texas' Revolution in 1836. If the Texans win, you have a new slave-holding republic whose only realistic chance of survival is the backing of the US. Great Britain and France are possible, however. Having Texas join the Union while Virginia seems to spawning a gradual manumission movement drastically alters the landscape. The Lower South will defintely want more slave states, the Upper South probably is okay with it (since most of the Texians come from this region), the North is against it, as OTL. Is this enough to alter events such that Texas joins in 1836-8 rather than 1845? Furthermore, Texas might demur from joining the Union for long enough to make idea unpalatable.
If the annexation of Texas is altered, so too is the Mexican-American War. If such a war comes before the South has adopted manumission, then slavery will still become an issue.
It's conceivable also that the Lower South choses not to adopt manumission: most likely the Upper Southern states sold large numbers of their slaves southward, increasing the concentration of African-Americans even beyond their OTL numbers. This probably only further incentivizes racial attitudes that motivate the defense of slavery, but the Lower South has no chance of numerically protecting itself in the US Congress. Virginia may well come to resent the 3/5s clause when South Caroliana manages to punch so far out of its demographic weight. This may be the moment for your "group of men of good intent" to settle the issue.
Manumission so adopted, however, will have more to do with economic change than political ideals. The radical abolitionist who so doggedly pursued the cause of civil rights will not emerge, since the Manumissionists will make the former seem even more extreme. However, the South will probably not be the monolithic block it became as the interests of lower class whites and planters begin to palpably diverge without the need to unite "in defense of race." Without the weight of Northern aggression, the restrictions of free blacks may evolve to less than those of Jim Crow (eventually). Certainly Lousiniana will be central to this evolution, given the history of the free black population there.
Without the Civil War, the issue of secession probably dies down but the primacy of the federal government will not have been confirmed in the crucible of the war. Western settlement (if it comes) may be troubled by the lack of a strong a Federal establishment as the war produced. This may, however, provide incentive to establish such a system.
Without the Mexican American war, Mexico may develop into some sort of stable regime, either tolerating Texas or re-absorbing it. Without the tensions of the Civil War, the history of Canada might be altered as well.