No. The Bible specifically says that the gospel message is to be taken to “all nations” and repeatedly emphasizes that salvation is for all. Chapter 8 of the Book of Acts contains a story in which a black man converts to Christianity.
Time to quote William Blake’s 1789 poem The Little Black Boy":
For when our souls have learn’d the heat to bear
The cloud will vanish we shall hear his voice.
Saying: come out from the grove my love & care,
And round my golden tent like lambs rejoice.
Thus did my mother say and kissed me,
And thus I say to little English boy.
When I from black and he from white cloud free,
And round the tent of God like lambs we joy:
Ill shade him from the heat till he can bear,
To lean in joy upon our fathers knee.
And then I’ll stand and stroke his silver hair,
And be like him and he will then love me.
I know of no Christian group that took this position, but it’s my understand that this was the Mormon position during part of the early years, though obviously not any more.
I’m pretty sure Christian Identity–and notions that only white people have souls, or that blacks are “mud people”–is a belief system that dates back only to the early 20th century. Slaveowners believed blacks to be inferior–commonly they portrayed them as “simple” or “child-like” people–but I doubt many antebellum slave owners would have claimed their slaves couldn’t go to heaven, “Christianization” of the blacks being (as mentioned) a major pro-slavery justification for the institution.
I also doubt antebellum Christians would have believed in a Whites Heaven and a Colored Heaven. For one thing, segregation was a post-slavery phenomenon; when you own people, you naturally want to keep a few of them close at hand (the “house servants”) to fetch you things and cook and clean and so forth. Under slavery, you didn’t have rigid separation of blacks and whites and separate water fountains and so forth; at least some slaves would live right there alongside their masters. And as to the afterlife, there are several Bible passages (I Corinthians 12:13, Colossians 3:11, Galatians 3:28) about the elimination of social distinctions (“Jews and Gentiles”, “bond and free”, Greeks and barbarians, even “male and female”) for those “in Christ”. Likely, an antebellum slave owner would have taken those passages to apply to the afterlife, not here and now, and also quoted Bible passages (Colossians 3:22-24, Ephesians 6:5-8) exhorting slaves to obey their masters here on Earth. I also seriously doubt there would be a widespread notion that slaves would still be slaves of their masters in heaven; in the New Testament, people aren’t even supposed to be married in the afterlife (Matthew 22:30) and I doubt 19th century Christians really believed Heaven would replicate here-and-now social relations like that.
The main point is, to an antebellum slave-owner, everyone would be free and equal…in heaven. And–for slaves–you’re supposed to be meek and humble and obedient in order to get to heaven. (So said the slave owners.)
I’m not qualified to identify the best source, but the Church of Jesus Christ of Latter-Day Saints (i.e. “The Mormons”) used to have a teaching that black people could not obtain the priesthood or Temple marriage, which were (and remain) required to obtain the highest level of afterlife reward. Now, blacks can get them. This is not exactly the same because the LDS have a complex system of levels of reward and the LDS consistently taught that blacks could be saved and “go to heaven” in a general sense, they just could not receive the ultra special you’re-so-holy heaven+ with complementary super-mansion.
Any LDS on the board able to provide references to authoritative teachings on this?
“Mud people” is associated with recent “Christian Identity” white supremacist/separatist/insurrectionist noise. See also “serpent seed.” It’s fringe stuff, and I guess it may not be all that old.
I say “insurrectionist” but these days I don’t know if there are any actual insurrectionists rather than just superannuated lads playing at forming “God’s Army.” I heard that during the Iraq War, the US Army started taking white power terror sympathizers they would have turned away before, so maybe these guys think they have a home in the GOP/TEA Party now? Or maybe the would-be Timothy McVeighs just end up in prison a lot.
Keep in mind that the weird American attitude to black people is not typical of the rest of the world, except South Africa. There may be xenophobia, but in general there were people of all colours of all ranges of education and culture and like any other foreigners, they were tolerated but not necessarily embraced by each European culture.
To go along with Bosch’s painting, also consider that Othello and Merchant of Venice figure prominently with Moor (black) characters, one married to a local (white) girl and the other hoping to. And in Othello’s case, he’s the good guy victimized by a sneaky white guy, and race seems incidental - he’s just another foreigner. Oh yes, and in Titus Andronicus, the queen gives birth to a black child proving her infidelity with her blackamoor lover.
IIRC, Idi Amin was noteworthy as being the first leader of liberated post-colonial Africa that was not a product of the European universities. Gandhi encountered racism in South Africa after he received a full university degree in England.
In both the Americas and South Africa, the deliberate de-humanization of the black underclass was part of a strategy to justify and ensure their continued subservience and put down any demands for equality.
I doubt that anyone in Europe centuries ago worried about whether black people went to heaven because they were not any more concerned about black people than about those greasy Spaniards or smelly French… 
(IF they were allowed into heaven, wasn’t anyone also?)
As for Americans, I’m betting the racist ones who believed in heaven probably also believed that the kind of “darkies” who would make it to heaven would be the ones who “knew their place” in both this place and that place.
(How about a perspective from the other side:)
You know, like some people say if you’re good an’ shit, your spirit goin’ to heaven… ‘n’ if you bad, your spirit goin’ to hell. Well, bullshit! Your spirit goin’ to hell anyway, good or bad.
[Why?]
Why? I’ll tell you why. ‘Cause, you see, doesn’ nobody really know that it’s a God, y’know, ‘cause I mean I have seen black gods, white gods, all color gods, and don’t nobody know if it’s really a God. An’ when they be sayin’ if you good, you goin’ t’heaven, that’s bullshit, ‘cause you ain’t goin’ to no heaven, 'cause it ain’t no heaven for you to go to.
[Suppose that there is a God, would he be white or black?]
He’d be white, man.
[Why?]
Why? I’ll tell you why. ‘Cause the average whitey out here got everything, you dig? And the n***** ain’t got shit, y’know? Y’understan’? So—um—for—in order for *that *to happen, you know it ain’t no black God that’s doin’ that bullshit.
—gangbanger Larry, interviewed by linguist William Labov, quoted in Pinker’s The Language Instinct, p. 29.