It's clunky, but this will typically work:
=IF(YourFormula=0,"",YourFormula)
In your case:
{=IF(IFERROR(INDEX('Census Sheet'!$H$1:$H$24,SMALL(IF('Census Sheet'!$N$3:$N$24="S",ROW($M$3:$M$24),""),ROW()-3),1),"")=0,"",IFERROR(INDEX('Census Sheet'!$H$1:$H$24,SMALL(IF('Census Sheet'!$N$3:$N$24="S",ROW($M$3:$M$24),""),ROW()-3),1),""))}
Edit: Because a zero result is not technically an error, the IFERROR will not work for it. I believe Tony was offering a solution that would be a little more elegant than my own, but for numeric values. Since you're seeking text values, try the above.
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