What you are looking for is an airtight vessel with one of three things connected to it to manipulate pressure:
1. A large piston or movable septum that can be manipulated to alter the internal volume of the vessel sufficiently. Since it is a contained airtight space, reducing the volume drives pressure up, increasing volume lowers pressure. While a speaker driver(s) could theoretically be used as a piston driven with variable direct current to control the diaphragm/cone position, it wouldn't be my first choice as making it airtight could potentially be a pain and DC to the voicecoil isn't efficient or recommended for long periods. Something like the old servosub or contrabass or whatever it was called with driver disconnected from servo motor and manipulated manually perhaps.
2. Both pressurized air tank and vacuum canister connected to your airtight vessel. By opening a valve one one or the other, you can increase or decrease pressure in the vessel as you add or remove air from it. Pressure tank is easy... think scuba gear. Vacuum canisters exist but are limited in pressure differential to just one atmosphere or so, and thus will be the limiting factor on how far you can manipulate pressure. Note that this is a one time use... if you deplete the vacuum canister or pressurized air tank you will have to disconnect and replace it with another.
3. Extending number 2 above, what you really want is an airtight vessel with a small air compressor attached to it to act as both the pressure tank and vacuum canister as above. If you use say a compressor capable of holding 10 atm of pressure, you want to fill it to 5 atm before connecting it to your vessel and creating the closed airtight environment shared between your vessel and the compressor tank. Note that both inlet and exhaust sides of the compressor should be connected to your vessel. By running the compressor pump you remove air from the vessel (and add it to the tank), lowering pressure in the vessel. Releasing air from the compressor adds it to the vessel and raises pressure (like adding air to a tire). Since you connected the compressor when it was half full, you can swing pressure in your vessel both ways at will and repeatedly. How far you can swing it depends on how large your compressor tank is and its pressure rating. It won't take much at all to swing the pressure over normal weather ranges, and you don't want to go far as a little pressure change on a large surface area creates a lot of force. Please be careful. You could easily implode or explode a fish tank.
I'd go with 3 above as it is the cheapest, most practical way of doing this. So long as air is moved from vessel to compressor tank slowly there shouldn't be undue turbulence. Running the compressor pump is generally a slow process. Just release it from the compressor slowly as well. If you are really concerned, you could place a baffle or diffuser inside the vessel so that you don't get a jet of air streaming into the vessel.