Since Sony Ericsson Xperia mini runs Android, you can use Fontomizer SP in order to download and install the Malayalam and Tamil fonts on your device. Once you launch it, select Tamil and Malayalam from the fonts list and download and install them. After that, navigate to your phone Settings > Display > Fonts and select Malayalam or Tamil as default. Alternatively, you can use Font Installer application developed by JRummy Apps.
Note: The phone needs to be rooted to use these applications, otherwise it won't work properly.