As I said in this question, there is a kingdom called "Shini" that helped Jarasandha according to Harivamsa.
I want to know what this kingdom is, or if there was simply a translation error to refer to a king as "the king of Shini."
The Shini Kingdom is most likely referring to the descendants of Śini, thier founder and who in turn is a descendant (grandson) of Vṛṣṇi. According to F. E. Pargiter in Ancient Indian Historical Tradition, pg.106:
Vṛṣṇi's youngest son Anamitra had a son Śini, and their descendants were called the Śainyas. All these are shown in the table opposite.
Here's the said table from the book showing the descendants of Vṛṣṇi, albeit a little confusing and may be inaccurate, since several other sources describe Vṛṣṇi's descendants a little differently:
As you can see, Lord Krishna and Balarama are also descendants of Vṛṣṇi. In the Bhagavad Gita, Arjuna refers to Lord Krishna as such.
You can access the book directly here: https://archive.org/details/ancientindianhis00parguoft/page/106