Welp @marvinwessels, you must be better at searches on AliExpress than I am, because I'm not having any luck locating a suitable replacement there.
What I can tell you, @traviscoles, is the battery is a fairly standard Lithium Ion. The numbers on the front of the battery, 753665 3.7V 2100mah, give you the physical dimensions, voltage and current rating of the battery. So you're looking for one that 75mm long, 36mm wide and 6.5mm thick. It's a standard Li-Ion voltage of 3.7V, and puts out 2100 mAh of power. So technically you can use any Li-Ion battery that has those dimensions or smaller. Since there is a direct correlation between battery size and power capacity, going with a smaller battery will reduce the available power. Oh, and you want to make sure you get one with three wires and a plug, although if you're handy with a soldering iron you could replace the plug yourself, but you do want to make sure you get one with three wires.
I actually located two suppliers where you could get the exact correct battery, but unfortunately there's a $150 shipping fee and a minimum order of 1,000 pieces, so I suspect that's not going to appeal to you. Sticking with it, though, I finally found a seller on Alibaba.com where you can actually buy just one of the batteries you're looking for.
[link|https://www.alibaba.com/product-detail/Lithium-ion-Cell-Supplier-Customized-Keyboard_1600613185985.html|Lithium-ion Cell Supplier Customized Keyboard Battery 753665 3.7v 2370mah Rechargeable Pure Cobalt Battery - Buy 3.7v Battery Bluetooth Headphone Battery,Nmc 3.7v 234ah Battery Cell,3.7v Lithium Ion Battery 153 Ah Product on Alibaba.com|new_window=true]
Interesting thing is that it's the exact same size but rated at 270 more mAh of capacity.
Hope that does it for you; that seems to be about all I can come up with.