Tsumego only solvable under NZ rules?
Yes, there are many examples if you look up a go "bestiary" (=

One such position:

$$B Status?
$$ -----------------
$$ | O O X . O X . .
$$ | O . X . O X . .
$$ | X X X O O X . .
$$ | . . O , O X . .
$$ | O O O O O X . .
$$ | X X X X X X . .
$$ | . . . . . . . .


If it is Japanese, Chinese, or AGA rules (basically anything without suicide), then white is dead. Black can fill all the inner liberties then capture the 3 stones like this:  

$$B Death for W -2,4,6 = Pass
$$ -----------------
$$ | O O X 1 O X . .
$$ | O 7 X 3 O X . .
$$ | X X X O O X . .
$$ | . 5 O , O X . .
$$ | O O O O O X . .
$$ | X X X X X X . .
$$ | . . . . . . . .


After capturing black has 3 liberties to white's 1.

If you are playing NZ rules however, the status totally changes:

$$B W is alive! W2 is a suicide play at 'a'
$$ -----------------
$$ | . 6 X 1 O X . .
$$ | 4 a X 3 O X . .
$$ | X X X O O X . .
$$ | . 5 O , O X . .
$$ | O O O O O X . .
$$ | X X X X X X . .
$$ | . . . . . . . .


Play up through W6 is seki. By being able to make a suicide move, white can make an eye inside and black does not have access to these extra liberties.  If black makes a move inside his own big eye space (playing at 5 at 6 for instance), he will not have enough liberties to win the capturing race, it will become an eye vs. eye seki.  

The amusing this about this position is that no matter who plays first in either instance, the status will not change, it may be left as is until the scoring phase of the game*. 
Whether white is scored as unconditionally alive or unconditionally dead will vary with ruleset, even though the position is identical.

*Clarification - Under NZ rules, black may wish to play out this sequence as ko threats, however the status of the group will not change based on who plays first.  Under non-suicide rulesets white does not even have ko threats.