I am recently engaged and bought my kallah a diamond. and I would like to have it set into a ring and give it to her. Can I do this in the Three Weeks?
You can have the ring set. However, giving her the ring would cause her an obligation of reciting shehecheyanu, which is customary to avoid in the Three Weeks.
For Ashkenazim, it is permitted to recite shehecheyanu on Shabbos, so you can give her the ring on Shabbos. However, it is not permitted to make a kinyan on Shabbos, including (according to most opinions) giving gifts.
Therefore, you should make a legal transfer to your kallah before Shabbos, by giving the ring to a friend and telling him to make a kinyan for your kallah. Having done this, the ring is legally hers. You can then give it to her on Shabbos, and inform her that the ring is already hers (from the time the kinyan was made). Upon receiving it, she makes the shehecheyanu blessing.
It is not appropriate to do this in the Nine Days.
Concerning the Shehecheyanu blessing, some authorities (such as the Vilna Gaon and the Taz) are lenient concerning the practice, and the Mishnah Berurah (551:98) therefore rules that one may be lenient on Shabbos.