Greetings Synthetic,
First a coke can is just not going to cut it. Based on a 125 mm ring spacing you will need a 1.25 mm shim to get the shots in the middle with adjustments bottomed out and likely 1.5 to 2.0 mm in practice. First however you might want to check that the adjustments are working properly. Using a large target with the aiming point at the bottom and at 25 metres wind the scope up and down and left to right firing a shot at each setting to see if the scope is doing what you tell it to. You might want to run the adjustments through their range first to distribute any lubricant in the mechanism. I gather this helps with scopes that have been idle for some time. After checking this and the other items above if you still want to shim it the shim should go between the scope base and the receiver ring at the front ring. You should never shim inside the rings. You will likely need longer ring screws.
It might be easier to just replace the scope.
Regards Grandpamac.
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