Easy. Just replace the word "happiness" with "good", "joy", "blessed", etc. All of which are valid and probably better translations. Which verse and translation are you referring to specifically?
God is the path to all things that are good, yes I fully agree with that. Joy is a very close synonym with the word 'happiness' and 'blessed' can mean happiness in some of maybe even many of the verses as I understand them, but I would also need to confirm with somebody who has a great understanding of the scripture. Here are some verses that I like from the King James Version that show us how sticking close to the Lord and having faith in God leads to happiness:
Psalm 37:4 Delight thyself also in the LORD; And he shall give thee the desires of thine heart.
Proverbs 16:20 He that handleth a matter wisely shall find good: And whoso trusteth in the LORD, happy is he.
Matthew 5:4 Blessed are they that mourn: for they shall be comforted.
Romans 15:13 Now the God of hope fill you with all joy and peace in believing, that ye may abound in hope, through the power of the Holy Ghost.
John 15:1-16 I am the true vine, and my Father is the husbandman. Every branch in me that beareth not fruit he taketh away: and every
branch that beareth fruit, he purgeth it, that it may bring forth more fruit. Now ye are clean through the word which I have spoken unto you. Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me. I am the vine, ye
are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing. If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast
them into the fire, and they are burned. If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you. Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples. As the Father hath loved me, so have I loved you: continue ye in my love. If ye keep my commandments, ye shall abide in my love; even as I have kept my Father's commandments, and abide in his love. These things have I spoken unto you, that my joy might remain in you, and
that your joy might be full. This is my commandment, That ye love one another, as I have loved you. Greater love hath no man than this, that a man lay down his life for his friends. Ye are my friends, if ye do whatsoever I command you. Henceforth I call you not servants; for the servant knoweth not what his lord doeth: but I have called you friends; for all things that I have heard of my Father I have made known unto you. Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and
that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you.