It is said that no monarch to sit the Crimson Throne has ever died of natural causes. Does anyone know how Queen Domina died?
It's not mentioned. Make something up for your game.
The curse also says that no monarch has sired an heir while on the throne. Technically that's true for Domina as well, because her son (spoiler alert! Sons!) were born before she took the throne.
"The Crimson Throne is not a prize to be won — it is a curse. No monarch of Korvosa has died of old age, and none have produced an heir while ruling."
So, since queen Domina did not break the curse, she didn't die of old age. It hasn't been stated how she actually died, or even how old she was at the time of her death. All we know is that she ruled from 4667 AR to 4686 AR and that her son(s) was (were) already born before she came to Korvosa.
We don't know when Eodred was born either, so we can't tell how old he was when his mother came to Korvosa. Still, he only ruled for 22 years and he was at least sixty when he died, so it is safe to say that he already was a young adult when he followed his mother to Korvosa, which would likely have made Domina at least 40 when she took the throne, making her at least 60 when she died.
The cause of her death is up to you, which is a good thing if you want to do something special with it. If not, it doesn't really matter, as long as it wasn't old age. In that case any disease will do. You could also have her be crushed by her own ambition: a big stone tumbled down on her from her Great Tower project while she was visiting the site to discuss whether or not it should be continued (since it was draining the city's coffers). Divine intervention, coincidence or foul play? You decide.