A combination of IntegerPartitions, RandomChoiceand RandomSample:
n = 30;
RandomSample @ RandomChoice @ IntegerPartitions[0, {n}, {-1, 0, 1}]
{-1, 1, 1, 1, 1, -1, -1, 0, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 0, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1}
Total @ %
0
You can also do
RandomSample @
PadRight[Flatten @ ConstantArray[{1, -1}, RandomChoice[Range[0, Floor[n/2]]]], n]
{-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0}
Total @ %
0
For large n, the second approach is much faster than the first.