It's an interesting question.
An obvious preliminary: whether or not all beautiful paintings are good, not all good paintings are beautiful. "Beauty" is sometimes quite beside the point in judging that a painting is good. But your question was about the converse implication.
Here's one sort of problem case. Suppose I see a painting that strikes me both as beautiful and as a genuinely good painting. I then find out that it's completely and totally unoriginal. It's slavishly derived from another painting. The extreme case might be a forgery, but highly derivative works raise the same sort of problem. The original might be both beautiful and a good painting; the derivative work might be every bit as visually beautiful as the original, and it might have taken enormous skill to create. It might be a good copy; it might even be a good forgery. Whether we want to say that it's a good painting is not as clear. We might think that to count as a good painting, a work has to have at least some measure of originality.
This brings us to a related but different point. If we say that something is a good painting, we're already making a different sort of judgment than when we say that it's skillful, for example. At least roughly, when we call something a good painting, we're saying that it has artistic or aesthetic merit. A painting could be skillfully-created kitsch; if it is, we're not likely to say that it's a good painting, even if we agree that the painter has skill. That's one reason why it's clear that if the question was "Are all pretty paintings good paintings?" the answer would be no. Kitschy things are often pretty, and the prettiness is often merely sentimental or, worse, manipulative. "Pretty" isn't the same as "beautiful," and prettiness isn't enough to make a painting good.
What if the painting is genuinely beautiful? Leaving aside issues of originality, is that enough to make it good?
It's not clear that we've escaped the problem we just raised for prettiness. It seems possible—you may even have your own pet examples—that a painting could aptly be described a beautiful, and yet be cloying or sentimental or manipulative. Once again, if that's so we may not call it a good painting, except perhaps in the technical sense. Beauty doesn't seem to be a guarantee of artistic merit, even if it takes skill to create a beautiful painting. And if we don't think a painting has artistic merit, we might well say that it isn't a good painting, whatever else it may be.
That said, things get murky here. Someone might insist that if something is cloying or manipulative or sentimental, it isn't genuinely beautiful. Someone who says this has probably already decided that "beauty" entails artistic value, and in that case your question would be settled by fiat. For my own part, I think that's a bad way to go. It seems that we really do use the word "beautiful" in a way that allows beautiful things to be of dubious artistic or aesthetic value. And if a genuinely good painting is aesthetically valuable, then the answer to your question seems to be no: there seems to be room for a painting to be beautiful and yet not to count as a good painting.