Is it correct to use the comparative adjective "blacker?"

What dictionary are you using? With a quick online search, I see the word "blacker" in these:

• http://dictionary.reference.com/browse/blacker
• http://en.wiktionary.org/wiki/blacker
• http://www.merriam-webster.com/dictionary/black (only the racial definition)
• http://oxforddictionaries.com/definition/english/black lists "blackest" in one of its senses, so "blacker" must exist.
• http://www.memidex.com/blacker

The reason that some dictionaries do not contain "blacker" and "blackest" is that "black" is considered to be an absolute adjective. This is the same reason you are not supposed to say "more perfect", "more unique", "whiter", "deader", or "fuller". See, for example, this web page.

There are lots of people who do not abide by this "rule". For example, Shakespeare, Procol Harum and the writers of the United States Constitution.

As technical terms, blackest and blacker are still going strong:

Acktar Black ™– world blackest coating – now 1% reflectance from FUV to FIR

World's blackest material unveiled

Blacker Than Black:

Black is black, right? Not so, according to a team of NASA engineers now developing a blacker-than pitch material that will help scientists gather hard-to-obtain scientific measurements or observe currently unseen astronomical objects, like Earth-sized planets in orbit around other stars. The nanotech-based material now being developed by a team of 10 technologists at the NASA Goddard Space Flight Center in Greenbelt, Md., is a thin coating of multi-walled carbon nanotubes — tiny hollow tubes made of pure carbon about 10,000 times thinner than a strand of human hair.

I used to see "Blacker" fairly frequently when film cameras were still the mainstay of photography.

Obtaining a "true black" was difficult with color negative film. So when a manufacturer would come out with a "new, improved" film they would often say, "Richer, more thoroughly saturated colors with whiter whites, and blacker blacks."

(What they used to call "white" and "black" fell short of the mark, and the new improved film achieves better results. But I would note, that then next generation of film might make the same claims all over again.)