Can I cite an accepted, pre-publication paper without DOI and the citations gets counted correctly? My situation: I got two papers underway and the second one was accepted only days after the first one. The second one cites the first one and, naturally, I want the citation to be attributed correctly. Currently, both publications are "accepted" and probably on the editor's desk or something.

How should I provide the bibliography information for an accepted paper? Can my citation still be accurately attributed to my first paper if I do not have a DOI for it (e.g. in Scopus)? Is there anything I can tell the editors of either journal to guarantee everything is going smoothly?

The field is solid matter physics/materials science.
It might be worth checking that neither journal assigns DOIs in advance - this is now supported by CrossRef, though not yet very common, and it's quite possible that they are able to tell you what the DOI will be now even if they don't normally inform you until later in the publication process. (For one thing, many journals issue DOIs based on an internal MS tracking number...)

Regardless of this, however, cite each paper as comprehensively as you can - accurate title, journal name, and clearly marked as "in press" or similar. This will make it easier for someone to know that there is probably a completed version out there somewhere, and give them the information they need to find it.

As I understand it, Scopus and Web of Science have a human involved in checking citations, not just an automated matching script, so hopefully they will be able to do the link manually when they see this. Both of them tend to lag a bit behind publication dates for citation records, meaning the chances are good that by the time the citation links are put into their database, the target will be online and citable.