A Green Olive Tree in God's House - Psalm 52:8

David  was trusting God to keep his covenant loyalty to him because God keeps his word. He is faithful. 

"A green olive tree"; which is a very choice and fruitful tree has:

• fatness in it
• produces an excellent oil
• is beautiful to look at
• delights in hot climates and sunny places
• is found on mountains
• we read of the Mount of Olives in the Bible
• is ever green and durable
• its leaves and branches are symbols of peace

All of the above characteristics are also applicable to truly righteous persons and believers in Christ who are:

•  the excellent of the earth
• are filled with the fruits of righteousness
• are fat and flourishing
• have the oil of grace - the anointing which teaches all things
• are a perfection of beauty - made perfectly comely through Christ's comeliness
• thrive under him - the sun of righteousness
• grow in the mountain of the Lord's house - the church
• their grace is incorruptible
• their leaf withers not
• they are rooted in Christ and ever continue
• they are the sons and daughters of peace
• their last end will be eternal peace.  

                                                                                                                                           adapted from  Gill's Exposition of the Entire Bible
A green tree is the emblem of prosperity.
I am safe and happy...I have been kept unharmed, like a green and flourishing tree...protected in the very courts of the sanctuary - safe under the care and the eye of God. A green tree is the emblem of prosperity.                                                                                                                                                                                                                                                                                     adapted from Barnes Notes

Those who by faith and love dwell in the house of God, shall be like green olive-trees there. And that we may be as green olive-trees, we must live a life of faith and holy confidence in God and his grace.                                                                                                                                                                                              Matthew Henry's Bible Commentary