Marius is the third child of Cygnus and Violetta Black. Over the following years, it is discovered that the poor child is a Squib. How he fares within is immediate family is unknown, but as far as his niece Walburga is concerned, he was a complete disgrace. Years later she blasted him off the Black Family Tree tapestry in her home, number 12 Grimmauld Place (BFT, OP6).
We can only conclude with certainty that Marius was born between one sister in 1915 and the other in 1920. However, we will narrow our guessing down a little by looking at the frequency of children in Cygnus and Violetta's family. They had children about every 2-3 years. So we can make the educated guess that Marius would have been born in either 1917 or 1918. For the purposes of the timeline, we'll place his birth as circa 1917.