UPDATE
My previous answer is no longer valid (since RC2), the resource is now marked as deprecated. (Thanks @Yossarian)
Proper way how to do this is now to use buildOptions/embed:
...
"buildOptions": {
  "emitEntryPoint": true,
  "embed": [ "9NLiZmx.png" ]
},
...
You must use the section resource in project.json, like this
{
  "compile": "*.cs",
  "resource": [
    "mapping.xml"
  ]
}
By default all code files in a directory containing a project.json are included in the project. You can control this with the include/exclude sections of the project.json.
Most sections of the project.json file that deal with files allow glob patterns, which are often called wildcards.
List of include/exclude properties
name                  default value
===============================================
compile                   
compileExclude            
content               **/*   
contentExclude            
preprocess            compiler/preprocess/**/*.cs   
preprocessExclude         
resource              compiler/preprocess/resources/**/*   
resourceExclude           
shared                compiler/shared/**/*.cs   
sharedExclude             
publishExclude        bin/**;obj/**;**/.*/**   
exclude              
More info: http://docs.asp.net/en/latest/dnx/projects.html#including-excluding-files
You can see a sample below:
Program.cs
using System;
using System.Reflection;
namespace ConsoleApp1
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var assemblyName = new AssemblyName("ConsoleApp1");
            var resources = string.Join(Environment.NewLine, Assembly.Load(assemblyName).GetManifestResourceNames());
            Console.WriteLine("List of Manifest Resource Names");
            Console.WriteLine("======================");
            Console.WriteLine(resources);
        }
    }
}
project.json
{
  "version": "1.0.0-*",
  "description": "ConsoleApp1 Console Application",
  "authors": [ "Alberto Monteiro" ],
  "tags": [ "" ],
  "projectUrl": "",
  "licenseUrl": "",
  "compilationOptions": {
    "emitEntryPoint": true
  },
  "resource": "9NLiZmx.png",
  "dependencies": {
  },
  "commands": {
    "ConsoleApp1": "ConsoleApp1"
  },
  "frameworks": {
    "dnx451": { },
    "dnxcore50": {
      "dependencies": {
        "Microsoft.CSharp": "4.0.1-beta-23516",
        "System.Collections": "4.0.11-beta-23516",
        "System.Console": "4.0.0-beta-23516",
        "System.Linq": "4.0.1-beta-23516",
        "System.Threading": "4.0.11-beta-23516",
        "System.IO": "4.0.11-beta-23516",
        "System.IO.FileSystem": "4.0.1-beta-23225",
        "System.Reflection": "4.1.0-beta-23516"
      }
    }
  }
}
Output
List of Manifest Resource Names
======================
ConsoleApp1.9NLiZmx.png