Ah......here's some conflicting information (how unusual with Minis).
According to the NSW Mini Car Club's "The Mini 1275 Book" it lists body prefix for Mk2 Cooper S as YG2S4, as AJ stated. However, they also list the Mk1 as YG2S1 - which is not correct as YG2S1 is Mini K.
Most other sources of info I have found list Mk1 as YKG 2S1, and Mk2 as YKG 2S2.
"Morris Cooper S - The Original Story" (auther unknown as I only have a photo copy of it) lists either prefix for both cars. ie: YG or YKG.
The BMC manufacturing schedule that I have a copy of lists YKG only.
The list of various Australian Morris ID numbers I have also only lists YKG for Cooper S (2S2 for Mk1 and 2S4 for Mk2).
Given that YG2S1 is Mini K and YG2S3 is Mini K - is it likely that YG2S2 would have been used for Cooper S? I don't think so.
As Stephen Dalton wrote in the Qld Mini Owners Club newsletter, Mini Mag, in July 2003, when identifying a Mk1 Cooper S - "Y=Australia, K=Morris Cooper (series), G= 1008cc-1399cc engine, 2S=2 door sedan, 2=2nd series of the model (the 997/998 Morris Cooper being the first)"
So, if true, it means that any Cooper or Cooper S should have the prefix YK, and G for the 1275cc Cooper S, as the K does not just mean Morris, but means Morris Cooper. YKA2S1 is 997 or 998 Cooper.
So why is the Mk2 Cooper S 2S4 - the fourth in the series? Perhaps the changeover model, sometimes called the Mk1.5, and which has neither BMC ID plate, nore Australian compliance plate, was considered by the factorty as the third in the series, so the "proper" Mk2 was the fourth. That's just my theory, but I reckon it makes more sense than a Mk1 Cooper S being YG2S1 or a Mk2 Cooper S being YG2S4.
Check other prefixes and this makes sense - YMA2S1 - Morris 850, YMA2S4 - Mini Matic, YMG2S1 or YG2S1 - Mini K, depending on diff ratio.
This might all sound a bit pedantic, but it is important when it comes to identifying a genuine Cooper S, particularly when good examples are now pushing $30,000 or more.
So, I still believe the plate with YG2 as the prefix is not from a Cooper S.
Why is there a hole right where the important part of the prefix should be?
Cheers,
Watto.

Mk1 Cooper S is always YKG2S2 , Mk2 Cooper S is always YG2S4 ( have a look at pic of Micks Compliance Plate , which is correct) . The K in Mk1 denotes Morris Cooper as opposed to Austin Cooper , but as no Austin Cooper or S where proposed to be built in Aus after 1969 , the K was ommited from all Mk2 Compliance Plates . I have owned many Mk2 Cooper S over the years and all have had the YG2S4 prefix both on the Compliance Plate and stamped into the radiator shroud panel . Its a common mistake made by fakers to stamp YKG2S4 on Compliance Plate .