Q: Need a battery replacement for my Macbook 13" Uni Late 2008.

You should still be able to buy a replacement battery

Since your MacBook5.1 is an Aluminum model, that may be

something to as the Apple Store or phone main Sales about.

Some models of battery are harder to get as product lines age.

A third party of known reputation (for RAM and other parts)

that several users have found reliable and trustworthy for

replacement or upgrade items is OWC or macsales.com.

Here is their site link for laptop replacement or upgrade parts

http://eshop.macsales.com/shop/powerbook-ibook-macbook/

The parts will vary if the MacBook you have, is not a MB5.1;

the other numbers matter: A1278 / EMC 2254 so be certain.

There are batteries listed at the online Apple Store...

Also there are sellers via Amazon, some may be OK.

•Apple battery:

http://store.apple.com/us/product/MB771LL/A/rechargeable-battery-13-inch-macbook -aluminum

•OWC battery:

http://eshop.macsales.com/shop/apple_laptop/batteries/MacBook_13_Unibody

•results of search google:

https://www.google.com/#q=Apple+MacBook+5.1+battery+replacement+Apple+Store

So there are products available.

Depending on Model Identifier.

Be sure to double check the MagSafe adapter, & power,

charging status, battery Cycles used, if doubtful.

Good luck & happy computing!

When having to use the power adapter for extended periods to run

the computer, and then replace a battery, the MagSafe power unit

may act up, so you could need to reset the System Management

Controller (SMC) should issue arise. That is a power manager; &

also holds other settings not affected by a NVRAM/PRAM reset.

•Intel-based Macs: Resetting SMC - system management controller

http://support.apple.com/kb/HT3964

•About NVRAM & PRAM:

http://support.apple.com/kb/HT1379

An older MacBook may require a new battery to be Calibrated;

though newer Macs may not; as power technologies changed.

•Apple Portables:

Calibrating your computer's battery for best performance

http://support.apple.com/kb/ht1490

If there is an actual issue requiring troubleshooting at some point

articles such as this one from Apple Support (online database)

may be of some help...

•Apple Portables:

Troubleshooting MagSafe adapters

http://support.apple.com/kb/ts1713

•Apple AC Adapter repair - ifixit:

http://www.ifixit.com/Device/Apple_AC_Adapter

The owc battery looks like a good unit with a better reserve.

While there probably isn't anything amiss with your power

adapter, sometimes with a power problem all components

should be checked over; but you need a known good battery

to really know if there may be an issue, anyway. Be sure to

fully charge the new battery before starting up the Mac.

Good luck & happy computing!

{edited 2x}

You are welcome!

How can i order an  Macbook late 2008 aluminium unibody apple battery online from apple store?

Did you search on Apple's site?  The old link is broken (this topic dates from a year ago) and it would not surprise me if Apple no longer had this part as support is discontinued for hardware older than 5 years.  Sometimes actually phoning Apple (in particular customer support instead of sales) can get somebody to check if they really, really do not have a part.  I know this has worked for some when trying to purchase OS installer discs for discontinued systems.

Vintage and obsolete products - https://support.apple.com/HT201624