The only mood stabiliser that has anti suicide propey is -

Lithium- * Lithium is a commonly prescribed medication for aggressive behaviors in a wide array of patients, including those with bipolar disorder, schizophrenia, conduct disorder, and intellectual disability. Its effect in increasing brain 5-HT function may be relevant in anti-suicidal propey. The required plasma concentrations are: For prophylaxis: 0.5-1.0 mmol/liter, increased occasionally to a maximum of 1.2 mmol/liter; For treatment of acute mania: 0.8-1.5 mmol/liter.