In general, DDR3 Core 2 motherboards from 2008 are not going to support any modern high-density DDR3. You're going to have to find low-density 4GB sticks and the best way to do that is to buy vintage used as new sticks like that are expensive.
BTW Avexir's data sheets are a joke as they don't mention chip density but they do say it's for "Support P55/H55/X58/H61/P67/Z68/Z77/X79/Z87"