I live in California I have a child with a man and within his family some issues have come up with his nephews children the father of my child and I are not married. The two children in question were in the process of being adopted by a blood related uncle, now that uncle is opting out of adopting and now the children will be put back into the system all other options such as grandparents or other family is out of the question. Is there any way that I could provide foster care for these 2 kids ? Please desperately seeking an answer time is running out for these two kids.

10. May single persons adopt?

Yes, single men and women may also adopt. In fact, approximately one-fourth of the children adopted from the public foster care system are adopted by single individuals.
http://www.childsworld.ca.gov/PG1302.htm

States would definitely rather have a child with their blood relatives. If you're not looking to go all the way to adoption, guardianship is another option

18. What is the difference between adoption and guardianship?

Adoption is the permanent legal assumption of all parental rights and responsibilities for a child. Adoptive parents have the same legal rights and responsibilities as parents whose children are born to them.

A guardian is someone appointed by the court to care for a child until he or she is 18. If you become a guardian, the court grants you the right to make most decisions regarding the child. A guardian is not a child's legal parent and may be subject to ongoing supervision of the court. Guardianship does not give all the legal rights and responsibilities of a parent to the guardian the way adoption does to an adoptive parent. The court can make a decision about guardianship whether the parent agrees.

As it is for many questions on this site, speaking with a family law attorney where you live is highly recommended. Good luck