int.rb

module Ext
  module Int
  
    def to_json
      # Do some encoding here.
    end
  end
end

::Integer.send(:include, Ext::Int)

JsonService.java

package org.bson;

import java.io.IOException;

import org.jruby.Ruby;
import org.jruby.RubyModule;
import org.jruby.RubyString;
import org.jruby.anno.JRubyMethod;
import org.jruby.runtime.builtin.IRubyObject;
import org.jruby.runtime.load.BasicLibraryService;


public class NativeService implements BasicLibraryService {

  private final String EXT = "EXT".intern();

  public boolean basicLoad(Ruby runtime) throws IOException {
    RubyModule ext = runtime.fastGetModule(EXT);
    new IntegerExtension(runtime, ext).redefine();
    return true;
  }

  public class IntegerExtension {

    private final String INTEGER = "Integer".intern();
    private final Ruby runtime;
    private final RubyModule integer;

    private IntegerExtension(final Ruby runtime, final RubyModule ext) {
      this.runtime = runtime;
      this.integer = ext.defineOrGetModuleUnder(INTEGER);
    }

    public void redefine() {
      // This doesn't work at runtime since:
      // Java::JavaLang::ClassCastException:
      // org.jruby.RubyFixnum cannot be cast to org.bson.NativeService$IntegerExtension
      integer.defineAnnotatedMethods(IntegerExtension.class);
    }

    @JRubyMethod(name = "to_json") public IRubyObject toJson() {
      // Do some encoding here.
    }
  }
}