I found a page of questions and answers about birth control on Tony Capoccia's Bible Bulletin Board. Mr. Capoccia seems to be a fan of John MacArthur, Charles Spurgeon, Jonathan Edwards, Thomas Watson, and J. C. Ryle. I gather that he would consider himself a Reformed Baptist.
In answer to the question, "Is contraception at all Biblical?" he gives five principles:
God said, to Adam and Eve, and to Noah's and his sons, (which would be a command for all generations after them), "Be fruitful and multiply" and He never rescinded the command.
God wants Christians to have lots of children because he was seeking "godly offspring"
God considers children a blessing from Him (something that will make us happy!)
God has the ability to "open and close" the womb causing conception or not.
God has commanded that all Christians, to include the Christian couple to live by faith.
Capoccio explains that the use of birth control is a matter of faith in God. Those with great faith will trust God with the timing and number of children. He explains how different methods of birth control show a lack of faith in God. In particular, the "rhythm method" involves abstinence, which is "prohibited in the Bible, except for special times of 'prayer' and then both must be in agreement."
People of weak faith may use birth control, but Capoccia tells us that he and his wife had great faith:
My wife and I both had great faith in God before we met. After we dated for almost a year we decided on marriage and both agreed that God could be trusted in the control of births. We let Him decide on the right number of children. A year after our marriage we had our first child, and then about every 14-18 months. We ended with six children, three boys and three girls. All are precious and very close friends. They range in ages from 13 to 20. Because of our great faith (a gift from God Himself) we have and are passing that faith onto our children, and they are growing rapidly in faith.
Evidently, that faith has limits:
After the sixth child (three C-sections, and three vaginal deliveries), the doctor said that another pregnancy could cause a great danger to my wife and the child. At that point, we felt it would be testing God to continue on with that new information. So we agreed to the tubal ligation, and felt this was from the Lord. We have seen that with each child, our income continued to rise to meet the new expenses. And now that the older ones are reaching the college age, it is amazing to see how God is meeting those needs.
Actually, the decision they made seems prudent to me, but the cynical part of me says if they really trusted God, they wouldn't engage in contracepted sex, and they would trust God to prevent a pregnancy. What they are saying, even if they don't realize it, is, "We trust God not to give us any more children, and we are going to trust him to work through the means available to us (tubal ligation) to bring this about." As a fan of Puritan and Reformed authors, I would think Mr. Capoccia would understand the doctrine of providence, that God accomplishes His sovereign will working through "second causes," including the decisions we make about contraception.