Usually, a PRG should be indistinguishable from a random generator. When a random generator produces $2n$ random bits, there should be more than $n$ bits equal to 1 about half of the time. Thus, your PRG would seem non random quite fast: a random generator would have probability only one in a billion to make more zeros than ones 30 times in a row, but your PRG will succeed every time.
That being said, you can also say: I want a PRG that is indistinguishable from a random source that outputs only sequences of $2n$ bits with no more than $n$ ones, but samples with uniform probability within these sequences. That kind of PRG is fairly easy to make. Take a one-way function $F$ that takes as input a sequence of arbitrary length, and outputs $2n$ bits (consider SHAKE, for instance). Then define $G(x)$ by computing $F(x||1)$, $F(x||2)$, $F(x||3)$... until you get an output with at most $n$ ones; this output is then your $G(x)$. If $F$ is a good PRG itself, then that $G$ will match your requirements.