Would it not be easier to just maintain a single set of staging or development keys rather than generating them for everything? IMHO you're losing configurability and not gaining much in security.
That aside, you're on the right track but I would do things a bit different.
export PROJECT=foo;
ssh-keygen -t rsa -N "" -C "[email protected]" -f ~/.ssh/id_rsa_${PROJECT}
That will generate named keys id_rsa_foo and id_rsa_foo.pub
Now you need to make your ssh config use it for github. ~/.ssh/config should have something like:
Host remote github.com
IdentityFile ~/.ssh/id_rsa_foo
User git
StrictHostKeyChecking no
You'll need to upload the public key to github. You'll have to figure this out for yourself using their API.
If you do all this correctly you should be able to git clone automagically.
#!/bin/bash
[[ -z "${PROJECT}" ]] && echo "project must be set" && exit 1
ssh-keygen -t rsa -N "" -C "[email protected]" -f ~/.ssh/id_rsa_${PROJECT}
chmod 400 ~/.ssh/id_rsa_${PROJECT}
echo $' Host remote github.com\n IdentityFile ~/.ssh/id_rsa_'${PROJECT}'\n User git\n StrictHostKeyChecking no' >> ~/.ssh/config
chmod 644 ~/.ssh/config
# do the github api stuff to add the pub key