Here’s a sample of what you ask for (type check can be added in last line to properly handle invalid cast exception to be more user-friendly):
public Action<object> Convert<T>(Action<T> myActionT)
{
if (myActionT == null) return null;
else return new Action<object>(o => myActionT((T)o));
}
May be you can give more details about the task though, because right now it looks a bit odd.