If she wants to sleep with you but she doesn't want a relationship, then the problem isn't with you being attractive. You have two options.
1. Be with her sporadically. Come over, have sex, sleep over some nights and be really affectionate, and leave afterwards other nights. If you guys are just screwing, you have no obligation to stay over. When you leave, just tell her you have to get up early and want to sleep in your bed or something like that. Don't tell her you changed your mind, but don't bring it up again either. If she asks you, tell her you're cool trying it her way. You can't slip up and let her know that you're still trying to convince her or the game is over. Be with her for a couple nights in a row, and then don't call her for a week. Date other girls
2. Take her at her word. Realize she's not willing to give you a relationship, but is willing to give you sex. Stop trying to manipulate her into asking for a committed relationship because you realize that even if she does agree in order to keep you, she won't mean it with all of her heart. As a worse case scenario, you'll lose out on the no-strings sex and on the relationship. Keep her for the sex, and continue your search for a committed relationship with someone else who actually wants one. Date other girls. Don't rub it in her face, but don't hide it either.
Notice that both solutions include dating other girls. I would pick option number two every time because that deals with things I can actually control instead of spending my time trying to make her change her mind.