I've been playing around with making my own custom joysticks recently. Just yesterday, I built this Atari VCS-compatible unit you see above using a Sanwa arcade joystick assembly and two Sanwa arcade buttons, both of which are available on Amazon.
I also used an old Bud project box from my dad's things for the housing, some screw-in rubber feet on the base, a cord from a non-working Atari CX40 joystick, and some scrap steel inside to give the stick more weight and heft.
I built it mostly so I could have a 4-way only joystick for maze games on the Atari 800. (The Sanwa joystick is switchable between 4-way and 8-way upon installation.) The result is absolutely incredible either handheld or set on a table, and my high score in Nibbler has gone through the roof.
On this joystick, both buttons do the same thing, although my next Atari model will probably have three buttons — one for fire, one for up, and one for down so I can play Asteroids on the 800 like a pro.