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Mathematica, 45 characters

Outer[List,d=Range[3]-2,d]~Flatten~1~Drop~{5}

Well. Generates all 9 coordinates, flattens the list and drops the centre.

Mathematica, 44 characters

Outer[List,d=Range@3-2,d]~Flatten~1~Drop~{5}

Well. Generates all 9 coordinates, flattens the list and drops the centre.

Mathematica, 46 characters

Outer[List,d=Range[-1,1],d]~Flatten~1~Drop~{5}

Well. Generates all 9 coordinates, flattens the list and drops the centre.

Mathematica, 45 characters

Outer[List,d=Range[3]-2,d]~Flatten~1~Drop~{5}

Well. Generates all 9 coordinates, flattens the list and drops the centre.

Mathematica, 27 characters

Outer[List,d=Range[-1,1],d]

Here is a different (straight-forward) approach using 30 characters:

Range[{i,j},{i,-1,1},{j,-1,1}]

Note that these produce nested lists (basically a matrix where each element is equal to its coordinates). If you don't want that you need to surround each answer in Flatten[...,1] for another 11 characters.

Mathematica, 46 characters

Outer[List,d=Range[-1,1],d]~Flatten~1~Drop~{5}

Well. Generates all 9 coordinates, flattens the list and drops the centre.