A remolded CBR may work for this
Determine the compaction curve of the material. Obtain Max Dry Density and Optimum Moisture values.
Say your Maximum Dry Density is 2.083 tonnes/m3 (I am Australian) with an OMC of 10.3% If you want to determine the CBR at 95% compaction, see what 95% of the MDD is, in this case it is 1.979 tonnes/m3. If you want to compact the material at optimum, you can do so, if you want you can compact it at what other percent of OMC you like.
You will need to know the CBR test material moisture content prior to adding any water, to ensure you know where you are from your compaction moisture content. Once you get your material to the desired moisture content, it is advisable to take another moisture content test to confirm you are at the moisture content needed. (How many more times can I say moisture content?) Keep this material in an airtight container, away from direct sunlight, you dont want to lose moisture.
You should already know the volume of your mold. Work out what your target mass of soil is for the WET density you want to achieve. For example a CBR mold with 2400ml volume you would need 5238.8g of soil compacted into the mold.
Target Wet Density = (MDD * Desired moisture content)
Target Wet Soil Mass = (Target Wet Density * Mold volume)
Divide this by the number of layers you will be compacting this material in. In Australia for a standard hammer it is 3 layers, so 1746.3g per layer is the target for the example. Compact each layer only with the amount of blows required to reach each layer height, ensuring on the last layer you do not compact lower than the mold. Do not trim off any excess soil from on top of the mold, you will need to get this level with the mold by use of a strike off bar or similar tool. It should not be difficult to do this with clayey materials at the optimum moisture content, gravel materials are another story.
You will want to determine your achieved CBR Wet Density and Compacted Moisture Content to determine your achieved dry density. From here on the CBR test will be the same as usual.