I don't claim to know the area, but I think I might have the answer. A note in the transcription of pre-1855 monumental inscriptions (North Perthshire Vol. 2, published by Scottish Genealogy Society) says: "The modern cemetery at Hillhead Logierait opened about 1950."
I hope this helps - but if researching Logierait, bear in mind that in former times it was a larger parish than it is now, with detached portions over a wide area. As well as the main churchyard, the MI transcriptions book lists five other burial grounds in various places.
Another resource for burial grounds is the database run by the Scottish Association of Family History Societies (
http://safhs.org.uk/burialgrounds.asp), which lists a total of nine for Logierait. (The discrepancy might be because not all of them have pre-1855 memorials.) This site doesn't have transcriptions, but it tells you where you can find these; it also has a location map for each burial ground, and indicates who is responsible for it.
Arthur