On each point, you must answer the following question: What's in it for the company?
Every programmer shall have two monitors
This is one of the harder items to quantify. How will the company benefit from you having two displays? Can you demonstrate that you're more productive with them? Can you propose a 3-month trial & demonstrate improvements in those 3 months?
Speaking for myself, I had to go back to a single-monitor setup. My desk is not configured in such a way that I could set up 2 monitors and not be constantly swiveling my head, or keeping it turned to one side. Result: months of neck pain. That pain negated any benefit I had from the extra real estate.
Every programmer shall have a fast PC
Are you currently constrained by your PC's performance? Do you spend a lot of time waiting for things to happen (builds) that would result in a significant increase in productivity, time or cost savings by upgrading the computer? Could a simple upgrade to the existing computer (SSD vs. traditional hard drive) be sufficient?
Every programmer shall have their choice of mouse and keyboard
Every programmer shall have a comfortable chair
These are a little easier to justify. Keyboard & mouse are inexpensive enough that replacing them shouldn't be a big issue. RSI can be extremely costly for a company - both in healthcare and lost productivity. If you can get better keyboards & mice that will reduce the risk or RSI, you can make this case.
As for chairs, you have similar concerns about health - posture, correct typing/working position, etc. That said, offices buy (or lease) their furniture in large blocks, and get a price break for that. So replacing the chair outright could be a hard sell. Making sure that the chairs aren't 15 years old, lack proper cushioning & support, etc. is easier. Getting someone on-site to make sure that chairs are properly set up is just as important.
Every programmer shall have quiet working conditions
Again, this is a difficult one because most non-technical managers do not understand that a 5-minute interruption can take a programmer out of his current task by an hour or more. Cube farms are standard in most companies. Giving programmers special treatment is generally not going to happen; the best you can hope for is getting your own cube "garden" (smaller than a farm) that's situated away from large walkways & areas with people who spend a lot of time on the phone. You can also try attempting to establish "office hours", a set block of time each day where people can approach you with "drive by" questions, but outside those hours they need to request a slot (unless it's a true emergency).
Ideally, we'd all have quiet working conditions. But the company needs to see a lot of financial benefit for the costs of giving programmers their own workspace that's isolated. Instead, pitch for a better location. Putting programmers next to the 10-person call center that takes 200 calls per hour, or next to the main aisle through the cube farm is a bad idea; relocating to a corner away from traffic, with a buffer zone between them and louder (by necessity) employees is more workable. Or you could pitch for improvements to the existing cubicle walls, perhaps more sound-deadening materials.