You just complete any 1 of the jobs in the Hitman Tier, it doesn't matter which 1 and the Diamond Ring could be 1 of the loot drops that you get when you complete a job. It's completely random.
Any of the Hitman tier jobs
Diamond ring is one of the vault collections you obtain doing jobs on the hitman tier of New York.See related mafia wars wiki link.its a random drop from the hitman tier
you do the jobs in the hitman job tier until you get it.
To get an emerald ring you have to do jobs in the hitman tier which could take a while.
hitman job tier
You can get the ties by doing the jobs under the hitman tier.
Hitman Job tier: Protect Your City From a Rival Family = Topaz Ring
disrupt rival smuggling ring in hitman tier of new york
Disrupt rival smuggling ring, new york, Hitman tier
Doing the Hitman Tier jobs will give you a chance to pick up the checkered tie.
The knitted tie can be found by doing jobs in the hitman job tier. there are several collections in the hitman tier. Be patient, it may be found after your next hitman job, or it may never be found. You could ask your mafia to "gift" it to you, or you could work a trade with someone in your mafia. (this seems to be the easiest way)
It is the "Protect your City against a Rival Family" job in the Hitman job tier.