You're right - there isn't any verse against birth control per se, but let's think about it another way.
Sexual bonding is a priveledge given by God to married couples, as Genesis says "the two shall become one flesh". The outcome of sex is life, and hence life is a product of the love between two person. We can broaden this to say that life is the result of love, since God created us out of love.
I believe contraception is a sin. As Christians, we should live our lives not around what we want but around what He wants. How do we seek His will? Well, we must diminish ourselves and let God dominate our lives, so that everything we do is done out of glorifying God. Since sex was created originally for means of procreation (meaning creation of life), it is a symbol of God's love for us, since He created us out of love. Sex without contraceptives, or natural sex, would likely result in life - which is sacred to God and fits into His plan.
I believe using contraceptives is limiting what God can do in your life. To be frank, it's taking matters into your own hands, so it's no longer in God's control. He gave us free will, and we use contraceptives to our own will instead of His will. And when we diverge from His will, we fall into sin.
Read this: "I don't want a child because I don't have the money because I don't have the time because I'M too old because I'M [insert excuse here], etc. But I do want to still have sex with MY husband, so God, this is MY plan for MY family, so - - - - DEAL WITH IT." Does't that sound like sin?
The sin of contraception to me isn't in the same category as that of abortion or euthanasia, but it is to me a sin of rebellion - taking matters into your own hands. If God doesn't want you to have a child, then He'll prevent it. But if it's God's will is for you to have a child, but you used contraceptives to your own free will, then you are limiting God in your life.
Pax Christi,
Vincent