...but you can if they are both medical specialties and you're applying in the same year. Virtually all of the medical subs (Cards, GI, H/O, neph, etc) are in the MSMP run by the NRMP, and the couples match is the same.

It depends on what fellowships you want to do. Depending on your field, getting a fellowship can be as easy as a couple of phone calls and an interview (many radiology fellowships, most non-NICU peds fellowships) to an extraordinary endeavor requiring outstanding performance, sterling recommendations, and significant research (some surgical fellowships like pediatric surgery).
Yeah, I guess one of would be doing the phone calls thing and the other some "moderate " endeavour.
If both the subspecialties go through the match but at different timelines, their match days being a week apart, a couples' match won't be possible, technically, right?
I think it would help people answer your question if you could be a little MORE vague and opaque.
It depends on what fellowships you want to do. Depending on your field, getting a fellowship can be as easy as a couple of phone calls and an interview (many radiology fellowships, most non-NICU peds fellowships) to an extraordinary endeavor requiring outstanding performance, sterling recommendations, and significant research (some surgical fellowships like pediatric surgery).
Actually, PICU, Pedi cards, pedi EM, pedi rheum, pedi heme/onc and pedi GI all have matches in addition to NICU and the last couple of fields will start this year or soon. Unfortunately, they mostly have different match dates and, unlike what appears to be the situation in IM, I know of no couples matching mechanism.
It is true however, that most fellowships (this has a lot to do with the hospital/med school) are not very competitive and it certainly is possible to do some negotiating or trying to go outside the match in pedi. No guarantees though, especially with the tougher-to-match programs and hospitals.