Answer:
Going with the NLT version, the objective pronouns are going to be: Lord, my, I, He, me, His, You, and Your. 
Explanation:
Since we know that an Objective Pronoun is the object of a sentence, and that it recieves the action of a verb, we can simply look for all the "he's, she's, my's, etc." Here is the passage below so you can see where the objective pronouns are: 
The <u>Lord</u><u> </u>is <u>my</u> shepherd;
    I have all that <u>I</u> need.
2 <u>He</u> lets<u> me</u> rest in green meadows;
    <u>he</u> leads <u>me</u> beside peaceful streams.
3     <u>He</u> renews <u>my</u> strength.
<u>He</u> guides <u>me</u> along right paths,
    bringing honor to <u>his</u> name.
4 Even when <u>I</u> walk
    through the darkest valley,
<u>I</u> will not be afraid,
    for <u>you</u> are close beside <u>me</u><u>.</u>
<u>Your</u> rod and <u>your</u> staff
    protect and comfort<u> me</u>.
5 <u>You</u> prepare a feast for <u>me</u>
    in the presence of <u>my </u>enemies.
<u>You</u> honor <u>me</u> by anointing <u>my</u> head with oil.
    <u>My </u>cup overflows with blessings.
6 Surely <u>your</u> goodness and unfailing love will pursue <u>me</u>
    all the days of <u>my</u> life,
and <u>I</u> will live in the house of the <u>Lord</u>
    forever.
Hope this helps! :)