Sources written in Old Norse and dating from the Viking Age (800-1100) are sparse, and insofar as I know, do not use the term blámaðr. There is a possible echo, however, in the Irish Fragmentary Annals. This was a chronicle written in Ireland, perhaps around 1030, but it survives only in a copy made from a copy in 1643. For the year 867, the chronicle famously reads:

[The two elder sons of Ragnall—possibly one of the historical figures at the root of the Ragnar Lothbrok legends] reached Africa, and they waged war against the Mauritanians, and made a great slaughter of the Mauritanians. ... Then they brought a great host of them captive with them to Ireland, i.e. those are the black men. For Mauri is the same as nigri [in Latin]; 'Mauritania' is the same as nigritudo. ... Now those black men remained in Ireland for a long time.

This is one of a very few sources documenting viking raids on Iberia and the Western Mediterranean. The whole episode is found under Annal FA 330. The original Irish uses the term fir ghorma, which has been translated here as 'black men'. This may well be a translation from Old Norse blámaðr. At the very least, it's the earliest attested historical event we know of where the word would likely have been used.

The Irish chronicler clarifies that these men came from Mauritania, although we should probably understand this as a generic term for North Africa between Morocco and Tunisia, i.e. the old Roman province rather than a specific geographic location or a contemporary state. Most tellingly, the chronicler used this as an opportunity to digress and show off that he could quote an old encyclopedia by Isidore of Seville, which asserted (spuriously) that Mauritania derived its name from the Greek word for 'black', which translates into the Latin 'nigri'. The chronicler also might have been playing with the concept of 'blue men' as mythical creatures in Gaelic mythology. I'm no expert on Irish mythology, so I can't say whether these figures already appeared in mythology in medieval times or only later. (The Wikipedia page has a lot of problems, including a reliance on sources written before 1935, and neither the tone nor the underlying assumptions bear up to the standards of modern scholarship.)

I believe that this is an authentic description of people whom Norse-speakers would have called blámaðr. And despite all the added layers of meaning that obscure what Norse-speakers would have thought of the word, I still suspect that the Norse language might actually lie behind the Irish chronicler's choice of terms. I'd certainly welcome any more concrete examples from the Viking Age proper, but that's probably as close as you're going to get.

Blámaðr is of course found in the prolific Old Norse writings that appeared just after the Viking Age. It appears to have been used both to describe people of darker skin tone—although not necessarily indicating the same range of skin pigment that modern English speakers describe as 'black' (which, of course, also depends on the speaker). It was also used to describe mythical creatures and seems in these cases to have often carried a negative, even demonic, connotation. This connotation, however, might derive from Christian binary pairs (good/evil, light/dark) rather than from pre-Christian Norse traditions. Richard Cole has written a really interesting article on these uses of the term blámaðr, which he's made available online here. I must admit, however, that I find his use of the terms 'race' and 'racial' troubling, since race is a very modern category and does not accurately reflect the worldviews of Viking-Age or medieval Norse speakers. But you're welcome to read his article and judge for yourself.

An important indicator for this is that although race is presumed to be something that is stable and inherited across generations, the meaning of the Norse word blár was changing. During the Viking Age, it covered a range of colors, what we would likely term black, blue, and green. It certainly did not translate precisely into Latin nigri, which seems to have covered black and dark browns. These kinds of discrepancies between Old Norse and Latin color terms posed problems for priests trying to acquire and wear the right colors for different liturgical seasons, and their questions and complaints are one measure used to judge the gradual transition of Old Norse color terms, from initially indicating depth and intensity of color to later indicating hue. Changing techniques for woad dying may also have been a stimulus for the separation of svarta to mean particularly 'black' and blár to mean particularly blue. Kirsten Wolf has a really interesting article on this, beginning on page 55 of Scripta Islandica 57.

So what does all this tell us about the blámaðr of the Viking Age? Well, perhaps nothing too definitively, but it does let us better understand the range of possibilities and shed some of our modern assumptions. It wasn't a racial term, since race is a modern category, although it was a physical description, perhaps even one with negative connotations attached. However, blár as a physical description didn't necessarily refer to the same skin colors that we would classify as 'black' today. It was used to indicate an intensity or depth of color, which could occur in many hues. Just as importantly, our one source from the Viking Age that could refer to blámaðr does not specify that skin color is at stake. The term could also be used to indicate textiles (i.e. dark clothing), and tattooing has also been suggested. Undoubtedly blámaðr was used to describe some people who came from Africa—among other figures both real and mythological—but were these the same as 'black' Africans as we might classify them today? Not necessarily so.