TL;DR We don't know, but probably they never got the chance to acquire one.
We know next to nothing about how the handful of Valyrian steel blades known to exist came to Westeros in the first place. Their distribution among the noble Westerosi Houses also doesn't tell us much. It doesn't seem to be a matter of wealth (in order to buy one), since the fabulously rich Tyrells (and their predecessors the Gardiners) are not known to have ever possessed one, yet the dirt poor Mormonts have had Longclaw for at least 500 years. It also doesn't seem to be a matter of political power since of the seven Houses that controlled the Seven Kingdoms pre-conquest only the Starks and the Lannisters have had Valyrian swords, yet the majority of the known Valyrian swords are distributed among several lesser vassal Houses.
This leads me to believe that acquiring a Valyrian steel blade is a matter of circumstance. Valyria is the only known source of Valyrian steel (House Targaryen has the distinction of being the only House to have possessed two Valyrian steel swords), so we can assume that the Westerosi blades exchanged hands (through war or artifice) until they reached their current owners. House Durrendan (and by extension House Baratheon) may have not had the good fortune of getting a chance of acquiring one.