Pat,
This is a common question and there is no real great solution. Although some face frame hinges give slightly smaller gaps than others, the difference is really splitting hairs. Salice is slightly better than most with a gap requirement of 5.2mm (5/32"). Keep in mind too that the 3/16 in gap requirement is per door. If you have a scenario where 2 doors are back to back the gap will need to be doubled (almost 1/2") to allow opening the two doors at the same time.
Also, the gap required between the door and the face frame is also much greater for compact style face frame hinges. This will be particularly noticeable at the end of a run of cabinets. Many people find this objectionable.
As Dan mentioned, using a standard Euro hinge and a face frame adapter mounting plate can produce very small gaps (1/8" or less). The problem here arises with the overlay. Without considerable modification to the face frame the maximum overlay will be somewhere between 3/4" and 15/16" depending on the hinge you use. If planned correctly this can also be worked out by hinging the doors on common frames back to back as in the example below. Each door overlays 11/16" with a 1/8" gap between doors.
I would do one of 2 things. First, I would build a small mock-up using compact hinges and show your customer the results. I might also suggest the customer go to the local big box store kitchen department and look at the displays. Most of them today use 1-1/2" frames with 1-1/4" overlay compact hinges to get that "full overlay" Euro cabinet look.
If the gaps she sees between the doors there are acceptable then you should be able to proceed using any compact hinge and give her the same results. This may be all she is really expecting.
Another point to check is the corner cabinet if there is one. If it is pie corner application then a 165 degree hinge would be best. You will need to do the same overlay planning here as with the other doors. There are a couple of solutions for this.
I might also ask if she would be interested in self close doors or soft close doors.
Best of luck.