Assign a static private ip to an EC2 instance

I want my server to connect to a db server (both on an EC2 instance). How can i give the db server a static IP address to use within EC2 without using VPC?

Elastic IPs are the only way without using a VPC. You can use a Security Policy to restrict all public traffic so you'd essentially have a private IP address (plus, these are free).

Edit: As pointed out by @ceejayoz, this incurs Internet bandwidth fees and is not the recommended method. Unless you absolutely cannot use VPC for some reason, use it. Otherwise, use the "internal" EC2 assigned IP or static as a last resort.