How to do a neutral special in Super Smash Bros. 4 with the right joystick

Yes, it is possible, but quite difficult.

From Smash Wiki (emphasis mine):

In Brawl and Smash U, functions that can be assigned to the C-stick are:
[...]
Special: Tilt the stick to do the special that corresponds to that direction. This is known as B-sticking. Tilting the stick in one horizontal direction while holding the control stick in the other causes wavebouncing. In addition, tilting the stick diagonally allows a neutral special, though the angle required for this is very strict.

The article is not wrong when it says the angle is very strict; I've been testing it and cannot get it to work reliably. But with a bit of practice I'm sure it's possible to confidently pull it off in combat.

Additionally, this also works with tilts and aerials when you set the function to "Attack":

Attack: Shortcuts to tilt attacks, and aerial attacks just like with the Smash function when in midair. In Brawl, tilting the stick in the direction opposite the player is facing will cause the character to do a neutral attack, whereas in Smash U, the fighter will turn around and attack with their forward tilt. Known as A-sticking. In both games, tilting the C-stick in a diagonal angle produces neutral attacks on the ground and neutral aerials in midair, with a wider angle than that do to neutral specials with the Special function: as such, this function also enables players to use neutral aerials without losing momentum.

I've been testing this, and it is much easier to do than for special attacks.

*Note that while it refers to the C-stick in the article, it explains that the right analog stick on the GamePad and Classic Controller function the same:

The right Control Stick on the Wii U GamePad and Classic Controllers also works like the C-stick for the Smash games these controllers are compatible with.