I’m looking for persuasive evidence that Cro-Magnon man (modern man) came out of Africa.
Well, my first suggestion is to stop looking for Cro-Magnon. As others have said, that name has fallen out of use among researchers. The issue is that you're not going to find much useful data using the wrong term. I'd suggest using more formal genus and species names--that'll both get you the data you're after, and cut through a lot of the garbage that crops up in this sort of discussion (it's not perfect, but it's a good first-order filter).
As far as modern humans go, this is a diverse and active field of study. There are two ways you can approach it: First, you can look at the modern data, through sites like Academia.edu, Google Scholar, and the like (you're going to have to put some cash into this--while you can get a lot of publications for free, others aren't going to be cheap). This will give you an understanding of the latest and greatest research, never a bad thing. Alternatively, you can get ahold of some resources on the history of this debate (Gould's "Mismeasure of a Man" comes to mind, as does "Darwin's Century"; I'll be honest, though, I haven't really looked into this topic in any great depth, as human remains aren't my thing). This question was one that many people debated, often quite pasionately, over the past few centuries, and it's only relatively recently that the modern consensus has emerged. A good book on the history of those debates would provided the data that finally ended them, which (considering the nature of the debates) is precisely the type of data you're asking for.
In general terms, the logic is that the First Appearance Datum for modern humans is in Africa. Attempts to move the point of human origins elsewhere have to contend with the fact that human remains in Africa extend to older times than human remains anywhere else. There's also genetic diversity--only a subset of humans left Africa, and frankly there's more diversity in Africa than anywhere else (I've never understood how anyone could claim that all black people look the same). Genetic studies have shown that this is because, again, only a subset of humans left Africa--meaning that all of us non-Africans share common ancestors (well, not QUITE true--there are a small number of out-of-Africa ancestors, as there were successive migrations out of Africa). So there are paleontological lines of evidence, and genetic lines of evidence.