IX. O God of my fathers, and Lord of mercy, who hast made all things with thy word, 2 and ordained man through thy wisdom, that he should have dominion over the creatures which thou hast made, 3 and order the world according to equity and righteousness, and execute judgment with an upright heart: 4 give me wisdom, that sitteth by thy throne; and reject me not from among thy children: 5 for I thy servant and son of thine handmaid am a feeble person, and of a short time, and too young for the understanding of judgment and laws. 6 For though a man be never so perfect among the children of men, yet if thy wisdom be not with him, he shall be nothing regarded. 7 Thou hast chosen me to be a king of thy people, and a judge of thy sons and daughters: 8 thou hast commanded me to build a temple upon thy holy mount, and an altar in the city wherein thou dwellest, a resemblance of the holy tabernacle, which thou hast prepared from the beginning. 9 And wisdom was with thee: which knoweth thy works, and was present when thou madest the world, and knew what was acceptable in thy sight, and right in thy commandments. 10 O send her out of thy holy heavens, and from the throne of thy glory, that being present she may labour with me, that I may know what is pleasing unto thee. 11 For she knoweth and understandeth all things, and she shall lead me soberly in my doings, and preserve me in her power. 12 So shall my works be acceptable, and then shall I judge thy people righteously, and be worthy to sit in my father’s seat. 13 For what man is he that can know the counsel of God? or who can think what the will of the Lord is? 14 For the thoughts of mortal men are miserable, and our devices are but uncertain. 15 For the corruptible body presseth down the soul, and the earthy tabernacle weigheth down the mind that museth upon many things. 16 And hardly do we guess aright at things that are upon earth, and with labour do we find the things that are before us: but the things that are in heaven who hath searched out? 17 And thy counsel who hath known, except thou give wisdom, and send thy Holy Spirit from above? 18 For so the ways of them which lived on the earth were reformed, and men were taught the things that are pleasing unto thee, and were saved through wisdom.
The Cambridge Paragraph Bible: of the Authorized English Version. (1873). (Wis 8:21–9:18). Cambridge: Cambridge University Press.
I think this passage is clarified by Solomon's personification of wisdom in the book of Proverbs, where he says to call wisdom your "sister" and understanding your "kinswoman" (female relative):
Proverbs 7:4-5 KJV - Say unto wisdom, Thou art my sister; and call understanding thy kinswoman: that they may keep thee from the strange woman, from the stranger which flattereth with her words.
The only other places I know of where Solomon personifies wisdom as a woman are in Proverbs chapters 4 and 8. In my opinion, they jibe better with the idea of a sister or aunt who have royal status (or at least royal connections) than an actual goddess on the one extreme, or a wife or female consort on the other:
Proverbs 4:8-9 KJV - Exalt her, and she shall promote thee: she shall bring thee to honor, when thou dost embrace her. She shall give to thine head an ornament of grace: a crown of glory shall she deliver to thee"
Proverbs 8:1-3 KJV - Doth not wisdom cry? and understanding put forth her voice? She standeth in the top of high places, by the way in the places of the paths. She crieth at the gates, at the entry of the city, at the coming in at the doors.