I can think of a few different ways to deal with it, and all involve using a high pass filter to retain the details, then recoloring to taste on new layers below the high pass filter layer, covering the reds and browns with mostly dark greens. Masking will play a big role in this process as well, and one of the ways I think I'd use it is toward the end of the process, mask out the couple, then make duplicates of the high pass layer until it has the ivy details in it that you want.
The recoloring in the ivy parts could be done by several means, and probably would work best using a little of all of them in various places for whatever's working best for that area: Brush while sampling colors, use curves to bring down the massive amounts of red, use hue / saturation to taste (I think darken somewhat and desat), etc.
In addition, I'd desat their clothing quite a bit to lose the reds, blues and greens that are now affecting them. It seems like he's got a lot of red in his skin tones as well, typical of old photos when they fade, so I'd bring that down and probably lighten him up just a bit with shadow / highlight. Beyond that, clone and heal a few nits, work on her face to even it out and bring back some natural color, and I doubt her lipstick was purple - that's probably just more color degradation, so I'd adjust that some with curves and maybe hue / saturation.
Figured I might as well give that stuff a try: