Getting *.amazonaws.com certificate

Let's say I am running a web service on an Amazon instance (AMI). This service talks to the HTTP requests coming from the client. As of now, I use public DNS of the AMI to make the HTTP request. For eg,

http://ift.tt/1aY1iWb

I now want to convert the HTTP requests to the HTTPS request. For that, the server needs to present its certificate to the client so that client can trust that it is indeed talking to the authentic server.

And this is where I am stuck. How do I get the certificate with a Common Name of *.amazonaws.com so that hostname in the request can match with the one in the Common Name in the certificate so that the client browser can happily accept the certificate and proceed further without giving any security related message to the end user.

I tried creating a self signed certificate with a Common Name of *.amazonaws.com however, since it is self signed (and thus not signed via a Certificate Authority), the browser asks me every time to trust the certificate and then only it proceeds further. This will be annoying for the end user and I want to eliminate that.

I do not see any option on the AWS console from where I can generate and download the required certificates.

Did anyone got into a similar situation?

Thanks. Piyush