Many rooting tools install the sqlite3 binary by default, but the pre-rooted rom on my SGS seems to be an exception, so here is a guide to install it manually.
You will need the SDK tools on your computer for this to work!
Connect the phone, bring up a shell and get root permissions:
$ adb shell
/ $ su
#
Find the device for the system partition:
# mount
rootfs / rootfs ro,relatime 0 0
proc /proc proc rw,relatime 0 0
sys /sys sysfs rw,relatime 0 0
/dev/block/stl11 /cache ext4 rw,noatime,barrier=0,data=writeback,noauto_da_alloc 0 0
/dev/block/stl10 /dbdata ext4 rw,noatime,barrier=0,nodelalloc,data=ordered,noauto_da_alloc 0 0
/dev/block/mmcblk0p2 /data ext4 rw,noatime,barrier=1,data=ordered,noauto_da_alloc 0 0
tmpfs /dev tmpfs rw,relatime,mode=755 0 0
devpts /dev/pts devpts rw,relatime,mode=600 0 0
none /acct cgroup rw,relatime,cpuacct 0 0
/dev/block/stl6 /mnt/.lfs j4fs rw,relatime 0 0
tmpfs /mnt/asec tmpfs rw,relatime,mode=755,gid=1000 0 0
none /dev/cpuctl cgroup rw,relatime,cpu 0 0
/dev/block/stl9 /system rfs ro,relatime,vfat,log_off,check=no,gid/uid/rwx,iocharset=utf8 0 0
/dev/block/stl3 /efs rfs rw,nosuid,nodev,relatime,vfat,llw,check=no,gid/uid/rwx,iocharset=utf8 0 0
/dev/block/vold/179:1 /mnt/sdcard vfat rw,dirsync,nosuid,nodev,noexec,noatime,nodiratime,uid=1000,gid=1015,fmask=0002,dmask=0002,allow_utime=0020,codepage=cp437,iocharset=iso8859-1,shortname=mixed,utf8,errors=remount-ro 0 0
/dev/block/vold/179:9 /mnt/sdcard/external_sd vfat rw,dirsync,nosuid,nodev,noexec,noatime,nodiratime,uid=1000,gid=1015,fmask=0002,dmask=0002,allow_utime=0020,codepage=cp437,iocharset=iso8859-1,shortname=mixed,utf8,errors=remount-ro 0 0
/dev/block/vold/179:9 /mnt/secure/asec vfat rw,dirsync,nosuid,nodev,noexec,noatime,nodiratime,uid=1000,gid=1015,fmask=0002,dmask=0002,allow_utime=0020,codepage=cp437,iocharset=iso8859-1,shortname=mixed,utf8,errors=remount-ro 0 0
tmpfs /mnt/sdcard/external_sd/.android_secure tmpfs ro,relatime,size=0k,mode=000 0 0
The important bit here is /dev/block/stl9 /system rfs which is needed for the next step.
Remount the file system rw (replace rfs and /dev/block/stl9 with the values from the output of mount):
# mount -o remount,rw -t rfs /dev/block/stl9 /system
Next, in a separate terminal copy the sqlite3 binary to the phone (can be obtained from the Super One Click package http://www.shortfuse.org/):
$ adb push sqlite3 /sdcard/
42 KB/s (24120 bytes in 0.557s)
Back in the original terminal, move the binary to /system/bin and set permissions:
# cp /sdcard/sqlite3 /system/bin
# chmod 4755 /system/bin/sqlite3
Finally, remount the /system filesystem read only again:
# mount -o remount,ro -t rfs /dev/block/stl9 /system