The part number of the actual connector on the board is marked "S2B-PH-SM4-TB" on the MKR1000 schematic (unmarked on the schematics for other MKR boards). The "S2" means side entry, 2 pin. The "SM4" means surface mount, which is not relevant to anyone looking to figure out which connector mates to it. My research indicates that all you need to know it it's a JST PH 2 conductor connector. All the PH series connectors are intercompatible regardless of the minor variations. You can find a lot of them on eBay with a search for "JST PH".
Ideally, all you would need to know is it's a 2 contact JST PH connector. All JST PH connectors are compatible with each other. Unfortunately, a lot of people (e.g., eBay, Aliexpress) are selling what they call a "JST PH 1.25", which has a 1.25 mm pin pitch. But all the JST PH have 2 mm pin pitch, so I don't know what that is. Maybe the JST GH? So you need to make sure the JST PH connectors you get from places like eBay specify they have a 2 mm pin pitch.