No, the Bible does not teach that we will have a second chance to receive Christ and be saved after we have died. If we've rejected Him in this life, we can only expect Him to reject us in the next life.
In fact, the Bible makes it clear that now is the time to decide for Christ, because we can't expect to have another opportunity later on. The Bible warns, "Man is destined to die once, and after that to face judgment" (Hebrews 9:27). The Bible also says, "Now is the time of God's favor, now is the day of salvation" (2 Corinthians 6:2). If we want nothing to do with God now, why do we think we'll want anything to do with Him later on? The devil says, "Delay," but Christ says, "Come now."
Pray for your cousin, and urge him to face the reality of his spiritual lostness. None of us knows how long we will have on this earth, and we may never have another opportunity to turn to Christ and trust Him alone for our salvation. Jesus said, "What good is it for a man to gain the whole world, yet forfeit his soul?" (Mark 8:36).
I suspect part of your cousin's problem is that he wants to have a good time, and he knows his life must change if he yields himself to Christ. But someday he will discover how empty his life is apart from God. Only Jesus can give us lasting joy and peace. Have you given your life to Him?