The best you can hope for is a compromise.
- get a secondhand stone and have it re-set. - get certified non-conflict diamond (or in my case, an Australian diamond) - get some other precious stone
The best one is to get hold of a family heirloom. Costs nothing and has far greater emotional value.
So, given that, instead of trying to use logic to sway someone who needs a ring, what are some tactics that appeal to emotion that can work?