The biggest reason for a noisey HVAC system is generally a poor return system. Many will try to use 1 return air duct which is centrally located in the house. The better alternative is to put 2 in and try to keep them in hallways if possible. This is the way I did my house and I cannot tell when it is running. Another problem may be an air handler too big for the system.
If you use a separate system you will have to put a return air duct in the room which is not desireable. A better alternative is to increase the size of the existing system (heat pump I pressume) and install another return air duct. An experienced HVAC contractor should be able to remedy this noise problem for you. Also DO NOT use duct board unless you like breathing in fiberglass particles. You probably cannot find it anyway. I haven't seen it used for years and it is probably against code also. Metal trunk lines with flex duct is the way. Trunk lines should be wrapped with insulation. HVAC should not be noisey. Good luck
If you use a separate system you will have to put a return air duct in the room which is not desireable. A better alternative is to increase the size of the existing system (heat pump I pressume) and install another return air duct. An experienced HVAC contractor should be able to remedy this noise problem for you. Also DO NOT use duct board unless you like breathing in fiberglass particles. You probably cannot find it anyway. I haven't seen it used for years and it is probably against code also. Metal trunk lines with flex duct is the way. Trunk lines should be wrapped with insulation. HVAC should not be noisey. Good luck