I just found that the Bingo quest line will get you admittance to Caras Galadhon if your rep isn’t up to what it should be. You can go freely in and out but still can’t use the stable (discover it anyway).

There is also a rope hanging to the left of the bridge after you cross over to the city but it only works for the quest that sends you to the city. Discover the stable while you’re there!