Yes, this is a tough one for English speakers.
Perhaps the most idiomatic way is to use the pronoun en or autre(s) itself:
There are some books. I have better ones.
Il y a quelques livres. J'en ai (d'autres) qui sont encore meilleurs.
I have good books and also some better ones.
J'ai de bons livres ainsi que d'autres qui sont encore meilleurs.
Notice that in the first one, since you provided a verb, there's something for en to easily attach to. This is preferable and so d'autres becomes optional. But in the second one, the two phrases are coordinated and there is no second verb, so there's not an obvious place to put en. Hence we need to insist on d'autres.
For your last sentence, note that in English I hear the sentence as a little tongue-in-cheek. When we contrast "good ones" vs. "other ones" we're playfully avoiding saying whether the other ones are worse, better, or equivalent, and that polite avoidance kind of avoids saying it's worse. Hence there's something unsaid and that usually makes direct translation harder.
In this instance, without a particular way of qualifiying or contrasting the other books, I think I would simply repeat the noun — but only to clarify, not because it's strictly necessary:
I have good books and also some other ones.
J'ai de bons livres ainsi que d'autres (livres).
With a longer noun phrase that you don't want to repeat in its entirety (e.g. with a relative clause), you can choose a key word to repeat.