try this:
awk '/two/{i++}i==2' file
with your data:
kent$ echo "onefish
onechicken
twofish
twochicken
twocows
threechicken"|awk '/two/{i++}i==2'
twochicken
note: if your file is huge, do this:
awk '/two/{i++}i==2{print; exit}' file
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