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Take a serious look at the products sold by Harken or other commercially available canoe/kayak hoists. I built my own and ended up spending close to what they sell for. Of course it depends on the height you are talking about too. That and the fact that they are primarily designed for use in a garage may limit your choices.
Harken makes good lifts, but I prefer to make my own. Since the demise of Webshots, my best photos of the pulley system I use are gone, but an example that's pretty close to my normal method is illustrated here (but the steel legs you see for supporting the canoe brackets when the rig is lowered is just a convenience feature):
Note that Harken recommends four-point lifting for canoes, but an easier method, and one which won't get misaligned due to rope stretch, is to support the canoe upside-down on bars, with those bars having a "wrap-around" feature that allows each to be lifted by a single rope. Some of the photos in the link provided show how to make such support bars.
You can eliminate the need for lots of pulleys by using a light-duty hand winch. You can get them for about $12 from Northern Tool, and models ranging from $20 to $25 are usually available at hardware stores.
The method I use relies on a single rope that's taken up by a hand winch (the system shown in the photos uses two ropes wound onto the winch, but that creates a problem which is described in the text that goes with the photos). That rope splits into two, with each fork passing through a separate lifting pulley. Each of those lifting ropes carries one support bracket of the kind I described above (two support brackets carry the boat). The only "rule" to follow is that when the main lifting rope splits into two, those two ropes must be fairly close to parallel. If they split into a wide "V", you'd need some additional pulleys to insure that the boat remains level during the whole phase of lifting, but in most situations it's easy to avoid the need for a wide "V" orientation of the lifting ropes.
If your store-bought pulleys use an aluminum rivet to support the pulley wheel, replace the rivet with a bolt or someday the rivet is likely to break and the pulley wheel won't turn.
Harken uses good-quality pulleys, but they are very tiny which means the rope must be very small diameter too. I'm not sure I'd expect such thin rope to last through as many seasons of outdoor exposure as something like 3/8ths of an inch or so. In either case though, replacing the rope at intervals is probably a good idea.
...... How far from ground is top of balcony rail ??
Will canoe remain supported in hoist at balcony/rail level until ready to lower again ?? (or do you intend to take canoe from hoist and store on balcony deck) ??
The word "balcony" makes me think of a smaller area (like associated with an apt.) rather than say a deck which can be much wider , how wide is the balcony ??
And then there is the need to suppoort a hoist . If the railing is the object that can support the hoist and the canoe ... pictures of it will be necessary .
If some other object is going to support the hoist and canoe , what could it be ?? ... pictures needed as well .
In any case , something can be designed that is safe and strong , easy to use as well . I might be able to assist in design if needed , I design many things and even build them in my profession .
By the way , you said "lower my canoe" , I'm just assuming you want to raise it also :-)