I think your supervisor might be best to advise you on the type of lit revew you need to do. If you do go for systematic review there are books out there on how to do systematic reviews in the Social Sciences, just google it. Also, you might want to look at youtube for academics discussing systematic reviews. Or check if your uni has an online research methods repository. I know what you mean though as not all current data in social sciences is in academic journals, I spent lots of time checking other sources such a government policy documents, charitable trusts research etc that are published as reports and don't always come up on searches but are never-the-less invaluable to informing lit reviews or adding depth to your background discussion.