DOI for a yet-unpublished paper
Assuming the formatting requirements of your journal say to include DOIs, I would do so. One of two scenarios seems most likely:


Paper #1 will appear in press (or online) before Paper #2 is published, at which point it is a trivial edit to change the in press citation to the proper published citation, with the DOI.
For some reason this doesn't happen, and Paper #2 sees the light of day before the DOI in Paper #1 goes live. For a relatively short span of Paper #2's life, readers won't be able to get to the DOI for paper one - but for what is likely the majority of the paper's useful life, the DOI given in the references section will be live, and will point to the published Paper #1.


It's only in that really brief span of time where a reader might try to access the DOI and not be able to. I think optimizing for that time (which may be zero) is counter-productive when you view a paper over its entire lifetime. At best, you have what is essentially an auto-updating reference. At worst, a reader goes "That's odd..." and emails you to see if they can get a preprint.