I suspected this was an allusion to pitch being used to coat the bottoms of ships for water-tightness, and a quick search of the resources shows this to be the case.
The kind of pitch I'm talking about is also called tar or bitumen, and is a petroleum product that is fairly hydrophobic (repels water). It is also ridiculously sticky, so it takes to surfaces very well. Because of these properties, pitch has been used as a water sealant in pools, for large storage vessels, as an adhesive, and to seal things like the bottoms of boats (Kirshnan & Rajagopal 2003).
Petroleum pitch is naturally black and thus the colour of most boats was black, but other colours were possible. To achieve alternate colours, an admixture of wax and mineral pigments was painted over the base layer to achieve vibrant colours, primarily for decorative effect. The following quote discusses the possible colours and the accompanying note directly discusses Homer's reference to 'black ships'.
It was usual to smear the seams or even the whole hull with pitch or with pitch and wax." Ship's paint was encaustic, i.e., wax melted to a consistency that could be applied with a brush and to which color had been added. The colors available, mostly mineral derivatives, were purple, white, blue, yellow, brown, green, red ; the brighter shades, such as red or blue or purple, were used for bowpatches and decorative effects. The hull could either be painted or left the black color it took on from its coat of tar[50] - (Casson 1971: 211 - 212).
- Thus Homer calls his galleys black. The hulls Procopius has in mind in the passage cited in note 37 above were obviously the color of the pitch with which they had been coated. - (Casson 1971: 212).
Jeffrey Emanuel wrote his MA thesis on this topic and delivered a workshop on analyzing material from an actual shipwreck. Both have been made available as open access publications, if you are interested. Specifically, page seven of the workshop PDF shows a painted reconstruction of a boat with colours intact and again addresses the same Homeric references to colour that you raised.
Bibliography
Casson, L. Ships and Seamanship in the Ancient World. Princeton, Princeton University Press, 1971.
Emanuel, Jeffrey P. Black Ships and Fair–Flowing Aegyptus: Uncovering the Late Bronze–Early Iron Age Context of Odysseus’ Raid on Egypt. Master's thesis, Harvard Extension School. (2015).
--- "Odysseus’ Boat? New Mycenaean Evidence from the Egyptian New Kingdom." (2014).
Krishnan, J. & KR Rajagopal. "Review of the uses and modeling of bitumen from ancient to modern times." Appl. Mech. Rev. 56.2 (2003): 149-214.
This question actually hits on something very interesting that you might not have aimed for! While not directly answering the question, it might interest you to know that colours in a culture’s vocabulary vary over time and specifically the study of colour useage in Homer’s writings were the source of that discovery. A good book on the subject is Through the Language Glass by Guy Deutscher.
Getting back to Homer: British Prime minister William Gladstone (he was also a researcher) noted a lack of color terms used in Homer and for instance Homer used porphyreos, which in later Greek roughly means "purple" or "dark red," to describe blood, a dark cloud, a wave, and a rainbow - suggesting a lack of vocabulary for colours.
He also describes the sea as oinops (wine-looking). Wine and water generally have quite different colours, and this has been taken to reflect a lack of vocabulary, not only poetic freedom. Specially, the word for blue did not exist in ancient Greek. Gladstone suggested that the ancient Greeks categorized colours mainly in terms of light/dark contrasts, rather than in terms of hue. Knowledge has advanced quite a bit since Gladstone, but his work on Homer pioneered the study of differences in colour vocabulary.
Since then, it has been found that many cultures/languages go through a similar pattern of vocabulary expansion related to colors, starting with red and then adding blue, possibly when blue pigment was discovered. The perhaps most famous linguists to discuss language development for colours are Brent Berlin and Paul Kay. Comparing color naming across languages, they observed some commonalities: If a language had only two terms, they were always black and white; if there was a third, it was red. A fourth and fifth would always be green and yellow (in either order); the sixth was blue; the seventh was brown; and so on.
There can thus be said to be a order in which vocabulary typically expands related to colours, often tied to if these colour terms are useful or can be produced as colourings. At the time when Homer’s ship description stems from, Greek colour vocabulary was not as rich as it is today, lacking for instance a term for blue. Therefore, colour descriptions might not always be taken literally.
Gladstone’s book on the subject is called “Studies on Homer and the Homeric Age”.