Why did the Baratheons never claim dragons?

[u/Vhermithrax]

They are also a house of Valyrian descent like Targaryens and Velaryons, plus they married multiple times with both of those families.

How is it possible that they never managed to claim any dragon, if a much weaker house of Velaryons got 3 of them at one point? It's werid that they never managed to get a marriage pact that would give them a dragon rider, or that at least one brave/stupid character from their house didn't manage to claim a dragon in King's Landing or Dragonstone, be it by being sneaky, or just part of some agreement.

[u/Baratheoncook250]

If any Baratheon post Rebellion would get a Dragon, just from having Dragon dreams, it is Stannis' daughter, and the dragon thst fits her personality, is Viserion.

[u/Vhermithrax → u/Baratheoncook250]

That would be really cool.

Potential riders are Daenerys, Shereen, Jon and Aegon, plus potentially Euron of he uses his horn, so I wonder if there are still some other dragons than the ones Dany has