Dedicated to the Lord Jesus Christ Who loved us, gave Himself for us, and washed us from our sins in His own Blood; and to the Church, which is His body.

These rivers of living water in John 7:38 are referring to the Holy Spirit and the effects He produces in the life of the believer. Galatians 5:22-23 says, "the fruit of the spirit is love, joy, peace, long-suffering, gentleness, goodness, faith, meekness, temperance." These qualities should flow out of us as a well. They should not have to be pumped. They will flow as we conform our thinking to God's Word.
Jesus speaks of bearing fruit in John 15 and declares that ". . . without me ye can do nothing" (John 15:5). This fruit is the product of the Holy Spirit, not our effort. Since "he that is joined unto the Lord is one spirit" (1 Corinthians 6:17), then this fruit of the Spirit is also what our born- again spirit produces. 
Our spirit always has these attributes regardless of what we feel in our emotions. Failure to understand this has caused many Christians to think they would be hypocrites to express joy when the truth is, they are depressed. It's only our soulish part that gets depressed. Our spirit is always bearing the fruit of "love, joy, peace, etc."
For a person who is seeking to walk in the Spirit, it is actually hypocritical to let our soulish emotions dominate our spiritual emotions. The truth is, our spirit is never depressed, just our soul. Those who understand this have the choice of letting their soul depress them or letting the Holy Spirit, through their born-again spirit, release the joy and peace spoken of here.
The "fruit" is not produced by the believer, but by the Holy Spirit, as we live in union with Him. Our part is to yield and trust; God's part is to produce the fruit.