A PropertyDrawer to show a popup field with a generic list of string for your Unity3d attribute

ExampleBehavior.cs

using System;
using UnityEngine;

public class ExampleBehavior : MonoBehaviour {
    [DropDownList("Cat", "Dog")] public string Animal;

    //using a method 
    [DropDownList(typeof(ExamplePropertyDrawersHelper), "methodExample")]
    public string methodExample;
}

public class DropDownList : PropertyAttribute {
    public delegate string[] GetStringList();
    public DropDownList(params string [] list) {
        List = list;
    }
    public DropDownList(Type type, string methodName) {
        var method = type.GetMethod (methodName);
        if (method != null) {
            List = method.Invoke (null, null) as string[];
        } else {
            Debug.LogError ("NO SUCH METHOD " + methodName + " FOR " + type);
        }
    }
    public string[] List;
}

PropertyDrawersHelper.cs

using System.Collections.Generic;
using UnityEngine;

public static class ExamplePropertyDrawersHelper {

  public static string[] methodExample() {
    var temp = new List<string>();
    temp.Add("Example");
    temp.Add("Second");
    return temp.ToArray();
  }

}

StringInListDrawer.cs

using System;
using UnityEngine;
using UnityEditor;

//This file should be in an Editor subdirectory

[CustomPropertyDrawer(typeof(DropDownList))]
public class DropDownListDrawer : PropertyDrawer {
  
  public override void OnGUI (Rect position, SerializedProperty property, GUIContent label) {
    var stringInList = attribute as DropDownList;
    var list = stringInList.List;
    if (property.propertyType == SerializedPropertyType.String) {
      if (list.Length != 0) {
        int index = Mathf.Max(0, Array.IndexOf(list, property.stringValue));
        index = EditorGUI.Popup(position, property.displayName, index, list);
        property.stringValue = list[index];
      }
      else {
        property.stringValue = "";
      }
    } else if (property.propertyType == SerializedPropertyType.Integer) {
      property.intValue = EditorGUI.Popup (position, property.displayName, property.intValue, list);
    } else {
      base.OnGUI (position, property, label);
    }
  }
}