where can I get a new battery for my apple watch series 2

I don't believe what SixFour391 said is entirely true. According to this:

watch Service Pricing - Apple Support

it will cost about $79 without an AppleCare+ plan.

You may also want to see:

watch Repair - Official Apple Support

If the battery is defective, you can schedule a Genius Bar appointment and get a replacement, under AppleCare+.

If the battery is simply old, then unfortunately it might be time to get a new one. Apple cannot replace batteries inside of their mobile devices. It's an entire device "swap".

Sometimes an old car needs a battery, sometimes the cost of repair outweighs the cost of getting a new one, entirely. This might be the case for you.

Yes, I think I may have been a little vague with my wording. I apologize for that.

When I said "Entire device swap", what I meant was you will get a new Apple Watch unit for the price of a "Battery Replacement" with AppleCare+, if the coverage is still active.

However if, with normal use, the battery has deteriorated and coverage has expired (as it may well have since you have a Series 2), there is nothing to do but buy a new AppleWatch.

I hope that lends some clarity.

Again, I apologize about any miscommunication on my part.