If you have the existing signing request, you can submit that again without any issues. Many registrars will actually keep a copy of your last csr for the purposes of renewals anyway. If that's not an option, a new csr is easly generated with:
openssl req -new -key <server>.key -out <server>.csr
Make sure you enter the Common Name (CN) as the address that'll be used in the URL to prevent clients throwing warnings.
One thing I am fond of doing on my own servers is to keep the old certificates around and organise my /etc/ssl/certs folder into years based on the date issued (or alternatively expiring). Helps me keep track of how many times the certificate has been renewed and when it's likely to be due for renewal next.
For reference, if you'd like a new key too, you'll want to do the following. In this case you will need to generate a new csr from this key.
openssl genrsa 1024 -out <server>.key
chown root <server.key>; chmod go-rwx <server.key>