Change the color of the picture background.

Just one more choice, what about Aperture App.

Does it have the ability to change the background color?

Aperture has advanced tools for adjusting and touching up photos. You can brush in locally changes of color, contrast, saturation, sharpness, dodge and burn, etc. So you could change the background color from yellow to white by brushing the saturation away. But Aperture is not meant as a tool for graphics compositing. It is a photo editor and organizer. If you frequently want to transplant parts of one photo to another photo and generally combine parts of photos into a new photo, then you would be far better off with one of the editors Terence Devlin listed.

If you plan on performing this type of editing on lots of photos eventually I've found that Photoshop Elements for Mac an excellent tools for removing backgrounds and adding new ones or your choice:

You need a photo editor for that, it's not a feature of iPhoto.

In order of price here are some suggestions:

Seashore (free)

The Gimp (free)

Graphic Coverter ($45 approx)

Acorn ($50 approx)

Pixelmator ($50 approx)

Photoshop Elements ($75 approx)

There are many, many other options. Search on MacUpdate or the App Store.

You can set Photoshop (or any image editor) as an external editor in iPhoto. (Preferences -> General -> Edit Photo: Choose from the Drop Down Menu.) This way, when you double click a pic to edit in iPhoto it will open automatically in Photoshop or your Image Editor, and when you save it it's sent back to iPhoto automatically. This is the only way that edits made in another application will be displayed in iPhoto.