In my textbook the following vocab is given, with 2nd tone for 难 in all of them.

难
难写
难看
难学

However skritter gives 2 possible tones for 难, 2nd and forth. In 难看 and 难学 it is marked as 2nd tone, but in 难写, 4th tone. Which is correct?

难 in 4th tone is 灾难的难 or 非难的难。
Hence, the meaning is different, it refers to "disaster", "trouble" or, as in 非难, "blame."

Yes, 难 can be both 2nd and 4th tone, but all the 难 in 难写、难看 and 难学 are 2nd tone.

Ok, thanks for your replies.

Probably 苦难 most common example of 难 in the 4th tone. It looks like, rule wise, if it's first char then it's 2nd, otherwise it's 4th. I seem to recall that being the case with some other characters too but can't summon them presently :)

That rule works most of the time, but I think it's better to associate the tone to the meaning rather than character position. This is kind of a crappy counterexample, but consider 艱難/艰难。

Yeah, after all you could just get it mixed up with tone sandhi I guess.

I corrected 难写 and 难学 in the Skritter database.