She wants to get married and she is asking about her wali (guardian) for the purpose of marriage?
Question

I want to ask who can be my wali for nikah?
My father is kafir and my mother and father are divorced. From my fathers side my male relatives who are al-Muslimeen include: 10 year old half-brother, uncle, two half-uncles, two half-grand-uncles.
From my mother's side my male relatives who are al-Muslimeen include: two uncles, grand-uncle. Also, Muslim sultan/ruler.
My mother is accepting to my nikah.
My nikah is to my cousin (my mother's brother's son - her nephew).
If I cannot find a wali from my family (because they refuse to the marriage or refuse to be my wali for the marriage), can I then proceed to a Muslim sultan/ruler to be my wali? Could my cousin who I am to marry be my wali for our marriage?
Also, please clarify to me the term 'usbah and evidence for it from Al-Qur'an and/or Ahadith/Hadith.
Please provide answer with evidence from Al-Qur'an and Ahadith.
Praise be to Allah.If your grandfather is your father’s father, then he is your wali. If he is not your father’s father, then your wali is your paternal uncle. It is stipulated that the wali should be Muslim, and none of your non-Muslim relatives has any guardianship, because Allah, may He be exalted, says (interpretation of the meaning):
“The believers, men and women, are Awliya’ ([plural of wali] helpers, supporters, friends, protectors) of one another,” [al-Tawbah 9:71]. 
Ibn Qudaamah (may Allah have mercy on him) said:
With regard to the disbeliever, he has no guardianship over a Muslim woman under any circumstances, according to scholarly consensus. … Ibn al-Mundhir said: There was consensus on this point among all of those scholars from whom we acquired knowledge.
End quote from al-Mughni (7/21) 
It is not correct for a more distantly related relative to be your wali for the purpose of marriage when there is a relative who is more closely related, unless the more closely related one refuses to give you in marriage to someone who is compatible and is pleasing in terms of his religious commitment and character. In that case, guardianship passes from him and his right to guardianship is waived, because guardianship of the woman is only given to the guardian in order that he may take care of the best interests of the woman under his guardianship, not to deprive her of that which is in her interests and to strive to cause her harm in order to delay her marriage and deprive her of her right to marriage. 
If the right of guardianship is taken from the direct guardian, does it pass to the next closest of the male relatives on the father’s side, or does it pass directly to the ruler or the one who acts in his stead, such as the qaadi (judge)? Concerning this matter there are two scholarly opinions, which have been discussed in the answer to question no. 171588 . 
In countries in which there is no Islamic legal system, the mufti or the shaykh of the Islamic centre, and the like, take the place of the Muslim qaadi. 
Secondly: 
The son of one’s maternal aunt cannot be a wali for the purpose of marriage; neither can maternal uncles or any other relatives on the mother’s side, because guardianship only belongs to the ‘usbah. 
The word ‘usbah refers to male relatives on the father’s side. They are entitled to be guardians with regard to marriage, in the following order: the father, then the grandfather, then the son [if the woman was previously married], then the brother, then the brother’s son, then the paternal uncle, then the son of the paternal uncle… A full brother is more entitled to be a guardian than a half-brother through the father, and so on with regard to paternal uncles and sons of paternal uncles. 
It says in al-Matla‘ (p. 366), in the chapter on ‘Usbah 
Al-Jawhari said: A man’s ‘usbah are his sons and his relatives through his father. They are called ‘usbah because they ‘asibu bihi, i.e., they surround him, the father on one side, the son on one side, the paternal uncle on one side, the brother on one side. End quote. 
To sum up our answer: 
Your wali with regard to your marriage is your Muslim grandfather, if he is your father’s father. If he is not your father’s father, then your wali is your paternal uncle. If your wali prevents you from marrying a man who is compatible and is pleasing in terms of his religious commitment and good character, and the rest of  your relatives on your father’s side follow suit, and do not give you in marriage to someone who is compatible, then you may refer your case to the Muslim judge or whoever acts in his stead, such as the shaykh of the Islamic centre, or an Islamic daa‘iyah in your area, so that he may enquire about the suitor and arrange your marriage if he thinks that he is suitable and fit for that. 
And Allah knows best.