Welcome to the CentOS fora. Please see the recommended reading for new users linked in my signature.
Please explain exactly what you did to remove sqlite. It should be possible to reinstall the package in rescue mode. The installed system should be mounted under /mnt/sysimage and the DVD installation directory can be mounted elsewhere, say /mnt/dvd, so it should go something like this after the boot from installation media in rescue mode:
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mount /dev/dvd /mnt/dvd
rpm --root=/mnt/sysimage -ivh /mnt/dvd/CentOS/sqlite-3.3.6-5.i386.rpm
Substitute x86_64 for i386 if on 64-bit.
If more help is needed please tell us what architecture you installed, i386 or x86_64, and explain exactly where you are running into trouble.