Before they invented the first climbing aids, human anchors were all alpinists had for protection.
This sounds exactly like something I would do. In fact, I've done it. When I was a kid I would rappel off of anything with anything, including the handrail of my grandparents deck, and I've actually been at the end of a rope with nothing but my father as an anchor while descending lower sloping alpine cliffs.
Sure it's not safe, but people don't go rock climbing or rappelling because it's safe, they do it because it's fun. There's always inherent risk with descending ropes. The challenge is to mitigate those risks by assessing the danger, and taking proper precautions.
First, you need to confirm the rail will hold your weight, easiest way to do this is to stand on it. If it'll hold your weight (which it will, because that's the whole intent of handrails...), then it's strong enough to hang off with a rope. Better yet, get you and the friend you're putting on backup to stand on the rail, because if you're putting the rope over it, then it's not holding just your weight, it's holding his too. A little bounce test will confirm it'll hold.
Second, tie your anchor as close to the bolts as you can. Shear strength is much greater than pull-out strength, if you tie your rope in the middle of the rail, then it's much like tying a two point anchor with too great an angle, you're actually going to put more force on the anchors than you would by hanging off only one side. If it were to buckle in the middle, it could pull the screws out. I think I recommend a clove hitch, because it won't slip to the side, otherwise I'd probably recommend a bowline on a bight backed up with a carabiner for ease and convenience of tying, the tail of the rope behind your knot is going to go back to your human anchor.
Third, tie in your sicherungsmann (belayer/security man). You could get him to hold you on a locked off hip belay, but since he's just acting as deadman anchor, you could just have him tie the other end of the rope around his middle and get him in a bomber stance, keeping the direction of pull in mind; if he's sitting on the ground with his feet propped up against a door frame or whatever and you take a fall, then the force is going to want to pull his butt off the ground because the railing will be higher than he is, and if he goes over then you're both in trouble. He needs to get his feet high enough so that if the rope goes tight, he's going to be properly braced for it.
That's my answer to your question as you've scoped it, now I'm going to offer some suggestions:
A better anchor would be to use your couch as a deadman anchor. Your couch is not going to go through your patio door if you turn it sideways and tie your rope around the middle.
Don't put the rope over the hand rail, run it under the bottom of the railing over the edge of the floor of your patio, the floor is stronger, and it removes any possible extension from your system. It does make getting over the rail and onto your rope a little trickier; you have to reach over the rail and grab the rope from the other side, tie into it, climb over the rail, squat down, take the slack through your descender, and then lower yourself over the edge, but it's more secure.
Be cautious on your first few goes. Don't dive over the rail, don't go fast, and don't try to stop fast. Slowing yourself down puts more force on the rope than just body weight. When you get close enough to the ground that a fall won't hurt, then you can fart around and swing and bounce on the rope to see how strong it is.
As long as you cover all your angles, you can have fun doing silly stuff with minimal gear.