The Bad News
As others have pointed out, Invisible Stalker is a monster and the stat block it uses is just not viable for a PC. You could always start tweaking the different parts of it to try to get something balanced but chances are it would never really pan out and your player would still be far too strong, or so saddled with drawbacks that he can't have ...
Ask the player "why?"
First step to solving these types of issues is asking why they want a thing. If the character wants to be invisible all the time just for the sake of that, just say no. If they like the idea of being able to attack from being hidden or that type of thing then you can help them out.
The Gloomstalker Ranger is invisible in darkness to ...
I told him no right off the bat...But he's extremely insistent about
Just tell the player "no," again; you are allowed to do that as DM
There are a number of reasons for this.
An invisible stalker is an elemental; PCs are humanoids1
The CR of an invisible stalker is 6; it usually takes 2 or 3 PCs of
level 6 to defeat an invisible stalker; the ...
The DnD world supports examples of various curses.
So your Tiefling could have came across a cursed artifact (either by stealing it, or receiving it, knowingly or not, as stolen property). It could have been a necklace, ring, knife, etc. Upon touching the object, it changed their skin tone as a punishment (to mark them as a thief).
Because the magic used ...
There aren't enough restrictions and requirements to narrow down the answer to a single build. However, I can go over your primary options and provide guidance for your decisions.
Class and subclass
For an intelligence based gish there's really only 4 options: Arcane Trickster Rogue, Battle Smith Artificer, Bladesinging Wizard, or Eldritch Knight Fighter.
The tiefling was born that way
According to the PHB, not all tieflings are red; quite the opposite, their skin might have "the full range of human coloration":
Their skin tones cover the full range of human coloration, but also include various shades of red.
5e low-level magic can only change your appearance temporarily, so it would be easier for you ...
You seem to be looking for very freeform control of an element. That is not normally achieved through the basic magic system (single-skill-per-spell magic, also sometimes known by the tautological title Magic magic). Nor does your description seem to match the magic of ritual paths in Basic Set (not to be confused with the other, standalone ritual path magic)...