The model number is not the prime identifier of the specific MacBook Pro build variables;
however you appear to be in luck by specification across several model build numbers
(see EMC, battery spec, and other; mactracker.ca database, everymac, & ifixit can help)
An example of a replacement battery that is said to be a replacement for several model
builds between several year designations, can be read about at iFixit.com. Other sites
may have something suitable. I did not look into macsales, but previously they had one.
https://www.ifixit.com/Store/Parts/MacBook-Pro-13-Inch-Unibody-Mid-2009-Mid-2010 -Early-2011-Late-2011-Mid-2012-Battery/IF163-019-1
Product code: IF163-019-1
Apple Part #: 661-5557
- For MacBook Pro 13" Unibody A1278
- Replacement laptop battery rated 5500-5800 mAh and 63.5 Wh.
- Apple's Model # A1322.
- Fits in 13" Macbook Pro Unibodies made from Mid 2009 through 2012.
Said to fit 2009, 2010, 2011, 2012 MacBook Pro 13-inch models with a variety of CPUs
& slight variance across original battery specs. You should double-check before buying.
Another example of battery option, from OWC macsales, similar spec:
•http://eshop.macsales.com/item/NewerTech/BAP13MBU65V/
http://eshop.macsales.com/shop/powerbook-ibook-macbook/
repair guides with info covering 13-inch MB/Pro:
https://www.ifixit.com/Device/MacBook_Pro_13%22
And you could also see an Apple Store or AASP authorized service specialist.
Hopefully this helps somewhat.
Good luck & happy computing! 🙂