There do not appear to be any studies to support there being a city with a zero incidence of suicide.
Suicide, sadly, seems to be a part of the human condition for some people, regardless of where in the world they are living.
This chart here gives an insight into suicide rates per country, with the highest rates reported in Guyana, Lithuania and Kazakhstan, a diverse continental spread.
A telling statistic, perhaps, is that Western European countries (by historical definitions) do no feature until Finland at number 20. This can perhaps be explain by the theory that suicide rates are highest in countries which have the biggest inequality gap, which seems to be supported by this listing.
In the 10 lowest ranked countries, 40% were located in the Caribbean, where suicide rates are traditionally low.
Another factor to consider in these statistics is the number of suicides that go unreported. In the UK alone it is estimated that 25% of suicides are not reported.