If I have 1g/dm^-3 of stock solution, how would I obtain 2cm of 300μg/dm^-3?

Stock solution: C₁ = 1 g dm⁻³ = 1,000,000 μg dm⁻³, V₁ = ? cm³
Diluted solution: C₂ = 300 μg dm⁻³, V₂ = 2 cm³

C₁ V₁ = C₂ V₂
V₁ = V₂ × (C₂/C₁) = (2 cm³) × (300/1,000,000) = 0.0006 cm³

To obtain 2 cm³ of 300 μg dm⁻³ solution, dilute 0.0006 cm³ of the stock solution to 2 cm³.
0.0006 cm³ is A more accurate method is to dilute 3 cm³ of the stock solution to 100 cm³, and then withdraw 1 cm³ of the diluted solution and further dilute it to 100 cm². At last, withdraw 2 cm² of the final solution.

I'm a big fan of applying dimensional analysis to chemistry and chemical engineering problems.
https://answers.yahoo.com/question/index?qid=20160219172026AAr3J7B

let's see how that would work out here.

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first... you need to understand the concept of what we're trying to do
.. (1) we want to calculate a volume of concentrate that we need to dilute
.. (2) we would then transfer that volume to a volumetric flask of the correct size and dilute to the line with solvent

second.. using DA to calculate volume concentrate

.. 2 cm³ dilute... (1 dm)³... .300 ug solute... .. 1g. .... .1 dm³ concentrate... . (10cm)³
--- ---- ---- ---- x ----- ----- x --- ---- ---- ---- x ----- ---- x----- ----- ---- ----- ---- x ---- ----- = 0.0006 cm³ concentrate
... .. ... 1.. .. ...... (10 cm)³... 1 dm³ dilute... .10^6ug.... ..... 1g solute... .... .. .(1 dm)³

the math simplifies to
. __ cm³ dilute * 300 / 1e6 = ___ cm³ concentrate

third.. since
.. (1) pipetting 0.6uL (0.0006cm³) requires practice, careful technique and something like this
.. ... .https://www.sigmaaldrich.com/catalog/product/sigma/z717283?lang=en&region=US
.. (2) and you would need a 2mL volumetric flask like this
... .. .https://www.coleparmer.com/i/corning-5641p-10-pp-plastic-volumetric-flasks-10-ml-1-pk/0611280
.. .. . only in 2mL.... not 10mL (see if you can find one on the internet!)

I'd suggest you choose a volumetric flask you can get your hands on, then plug in a different number into that equation above, then choose a pipette + tip that can give you the correct amount, then add your concentrate to the flask, then dilute to the line and mix appropriately, then pipette 2mL of your dilute solution into where-ever you need it.

example.. let's choose that 10mL volumetric flask
.. volume concentrate = 10mL * 300 / 1e6 = 0.003mL = 3uL
.. find a pipette + tip that can handle 3uL
.. pipette 3uL into your volumetric flask
.. dilute to the line with solvent
.. stopper, invert a few times to mix, etc
.. pipette 2mL of the dilute into where-ever

EDIT...OK, I was in a hurry and messed up...Corrected Calculations:

1 g/cm^3 X 1000 mg/g X 1000 ug/mg = 1X10^6 ug/dm^3
1X10^6 ug/dm^3 X V1 = 300 ug/dm^3 X 2 cm^3
V1 = 6X10^-4 cm^3 = 0.6 uL

You could use a micropipetter to add 0.6 uL to 2 mL of your water. Alternatively, as others have said, doing a couple of different dilutions is another approach.

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I am guessing that you need 2 cm^3 of that solution.

Use the relationship:
C1V1 = C2V2

1 g/dm^3 X (1000 ug/g) = 1000 ug/dm^3. So:
1000 ug/dm^3 (V1) = 2 cm^3 / 300 ug/dm^3
V1 = 0.6 cm^3

So, you would take 0.6 cm^3 (0.6 mL or 600 uL) of the stock solution and add water (or buffer) to give you a total volume of 2 cm^3. The volume of water added would be 1.4 cm^3.