I was raised fundamentalist. At the small private school I went to (which was really just a wing of our church) I did my share of Bible reading. I have read it cover to cover at least half a dozen times and memorized large chunks of it. In addition, I had mandatory bible study classes each year, which continued at the religious college that I attended. I did my homework. But listening to most of the fundies you hear wailing around the internets, I wonder if they have ever cracked the cover.
I can tell you a few things with certainty. There is no prohibition on artificial insemination. There is nothing banning lesbians from having children. In fact, there is really nothing about lesbians at all. The context of all of the anti-gay verses is hotly disputed, but they all reference (if anything) man-on-man coupling.
But maybe you are better than the average Christian and you expect everyone else to be too. After all, the Bible doesn't mention abortion or gun control either but that doesn't mean that they don't make Jesus cry. Are there any Biblical alternatives to artificial insemination? Why yes. Yes, there are.
This is a passage from Genesis 30, TNIV:
1 When Rachel saw that she was not bearing Jacob any children, she became jealous of her sister. So she said to Jacob, "Give me children, or I'll die!" 2 Jacob became angry with her and said, "Am I in the place of God, who has kept you from having children?" 3 Then she said, "Here is Bilhah, my servant. Sleep with her so that she can bear children for me and I too can build a family through her." 4 So she gave him her servant Bilhah as a wife. Jacob slept with her. 5 and she became pregnant and bore him a son. 6 Then Rachel said, "God has vindicated me; he has listened to my plea and given me a son." Because of this she named him Dan. [a] 7 Rachel's servant Bilhah conceived again and bore Jacob a second son. 8 Then Rachel said, "I have had a great struggle with my sister, and I have won." So she named him Naphtali. [b]
9 When Leah saw that she had stopped having children, she took her servant Zilpah and gave her to Jacob as a wife. 10 Leah's servant Zilpah bore Jacob a son. 11 Then Leah said, "What good fortune!" [c] So she named him Gad. [d] 12 Leah's servant Zilpah bore Jacob a second son. 13 Then Leah said, "How happy I am! The women will call me happy." So she named him Asher. [e]
14 During wheat harvest, Reuben went out into the fields and found some mandrake plants, which he brought to his mother Leah. Rachel said to Leah, "Please give me some of your son's mandrakes." 15 But she said to her, "Wasn't it enough that you took away my husband? Will you take my son's mandrakes too?" "Very well," Rachel said, "he can sleep with you tonight in return for your son's mandrakes."
16 So when Jacob came in from the fields that evening, Leah went out to meet him. "You must sleep with me," she said. "I have hired you with my son's mandrakes." So he slept with her that night.
So in summary, if you can't have babies, just get the man of your choice (preferably your husband, but not specified) to rape your servant. God says thats just as good. However, its quite possible that your sister (looking at you Elizabeth) is getting more babies from the same man. Some servants are just more fertile. In that case, you may need mandrake
Mandrake is a root that was commonly used in pagan rituals to increase fertility. It also makes great currency if you need to but a gigilo to stud for you.
Hope this advice is helpful. At least, until the Bible replaces the Constitution as our fundamental law. Then its not advice, its mandatory.