Use your down-arrow key to get to the bottom of the rope (Cyrus can't fall off with that key). Use the left and right arrow keys to make him swing. Hold down one until he gets as far as he's going to in that direction, and then switch, and hold down the other arrow key while he's going the other way, to build up his momentum. Switch back and forth as appropriate, until he builds up quite a swing. When he's really swinging wildly, at the end of one of his forward swings, hit the jump key and the forward arrow key, and he'll really sail towards the next rope/ledge/whatever.