There are various degrees of a "zoned" HVAC system.
A simple zoned system will include motorized dampers in the ducts to direct air where it is needed. e.g. If one room is too cold, but the other ones are fine, the system will shut the dampers to the other rooms, and then fire up the heater so just the one room is heated.
More sophisticated zoning systems for larger house will include multiple heating/cooling units (e.g. one for the upstairs and one for the downstairs).
Zoned systems can also work on a schedule. (e.g. keep the downstairs of your house comfortable during the day, but direct all of the airflow upstairs at night.)
As you can imagine, the control systems for such a unit get pretty complex. Motorized dampers everywhere, control lines to all the dampers, thermostats in the various rooms. It all adds up to a lot of money. It is also a lot of stuff that can break.
Because of the complexity, most HVAC contractors will avoid doing a zoned system unless absolutely necessary. It is usually easier to install a big air handler (enough CFM to cover the whole house), and then put a few manual dampers (1/10th the cost of motorized ones) and tweak them until they are right.
EDIT: Another option to consider is a multi-split system. Instead of having all your ducts connected back to one central air handler unit, each room/area has its own indoor unit, with its own fan and thermostat. All of the indoor units have refrigerant lines that are connected to the outdoor condenser unit. Each unit can heat/cool independently. Some systems even allow simultaneous heating and cooling (good for server rooms in an office building). Because they are ductless, they are a good fit for retrofitting a house with no ducts. They do not make a lot of sense in an existing house that is already ducted, though.
This problem can be multi-faceted. Someone could guess all day long as to what the problem(s) is / are and not even come close. Air conditioning isn't something to guess at. It's like having a rattle on a car and taking the approach of replacing one part at a time to find the rattle. It would be cheaper to just buy a new car. ( I give that as an example you can easily understand. You probably won't like it but the truth is always hard to swallow when it involves money.)
This is why air conditioning is a billion dollar plus industry. It's unlikely you will solve this kind of problem on your own as a "do it yourself" solution.
Sure you can do the things suggested like window coverings but if the problem is a "system performance" problem it's unlikely to make much difference.
With all of this said... if the problem isn't found and corrected it is quite possible to spend all kinds of money wastefully. The air conditioning business isn't known for being "easy". Certainly some repairs can be but issues such as these can be quite difficult.
It's quite possible it's just too hot. If out door temps are up over 110 degrees and you're hitting 76 inside... well if you think the AC is not working go outside for 15 minutes or so and walk back in. That dial on the wall is to turn the unit on and attempt to hit the desired temperature that you set. But there is no guarantee that it will. Air conditioning (depending on climate, location and design of the system) is mostly designed to lower the temperature 20 degrees from that of outside. (again this depends upon design of the system.)
Air conditioning loses noticeable capacity at 105 degree outdoor temp. again depending on climate and design of the system. Air conditioning isn't a cookie cutter appliance. One size does not fit all.
If out door temps hit 110 or more, be happy with what you get and reduce indoor loads. Plasma TV's, specialize computer equipment, excessive incandescent lighting, halogen lighting, excessive people loads (more than two per room), etc. will only add to your discomfort.
I am a licensed HVAC contractor with over 20 years experience in Residential HVAC systems. Serving the Katy & Cypress Texas area (suburb of Houston)
Best Answer
Ducts shouldn't be held (or even sealed) with tape. That's an obsolete technique. For a quick repair, you might find that aluminum foil tape is robust enough to hold. Otherwise, clean the duct surface and use clear 100% silicone. Give it at least 4 hours to cure. 8-12 would be better. Note that silicone isn't paintable, so if you need that you might consider urethane caulk.
Really, an in-duct damper at the split to each room is best. You may need to get a tinbender involved, as special tools and techniques are sometimes required.
Finally, consider switching the occupants of the rooms. Sometimes the best solution is the simplest one.