By default docker get installed under /var/lib/docker . If you don't have enough space there then you might have to do following

docker_change_location.sh

#Check if /var is getting filled
df -k
#If /var space is not more than 50GB do following
sudo su
#Stop Docker
service docker stop
#Copy all files to folder that have enough space
#usually in linux boxes there is enough space under /export 
#Create a dummy directory 'mkdir /export/apps/docker'
cp -R /var/lib/docker/ <Your other folder>
#Create backup
mv /var/lib/docker/ /var/lib/docker.backup
#Create softlink so in above example it would be 'ln -s /export/apps/docker/ /var/lib/docker'
ln -s <Your other folder> /var/lib/docker
#Start docker
service docker start
#Run following command to check change (look for Data file and Metadata File value)
docker info
#If everything is fine then
rm -rf /var/lib/docker.backup