I have talked to many women who say they have trouble finding lovers, even for casual or FWB relationships--though not, perhaps, for the same reason that men have trouble.
Most people believe that women could probably walk up to guys and cold-solicit for sex and easily find a partner. So why don't they? There's a saying: "Men's greatest fear is that women will laugh at them. Women's greatest fear is that men will kill them." Violence against women, especially around sex, is a lot more common than most folks think it is. A man asking random women for sex will probably hear a lot of "no"s; a woman asking random men for sex may end up being assaulted.
University of Michigan psychologist Terri Conley has done a series of studies [1] in which he tried to gauge how easy it was for men and women to find casual sex, and how likely they were to do it.
Her research suggested that the differences in willingness to have casual sex wasn't down to any of the pop evo psych explanations like "men want to spread their seed, women want companionship" or any of the other pop-psych answers, but rather down to issues of pleasure (women are more often hard to satisfy sexually) and safety. When controlling for those factors--that is, when setting up a situation in which a woman could solicit for sex knowing she would be safe and would likely find the encounter pleasurable for her--women and men are about equally likely to want, and respond to, sexual offers.
Also, it turns out the notion that men will always say yes and men are always willing and ready to hop in the sack isn't true. It's a popular idea, but it neglects the fact that men are about equally likely to want monogamy when compared to women, and that men do actually value things over and above just sex. So no, women are not assured of getting a "yes." (In fact, this mirrors my own experience; I say "no" more often than I say "yes.")
[1] Conley, T. D. (2011). Perceived proposer personality characteristics and gender differences in acceptance of casual sex offers. Journal of Personality and Social Psychology, 100(2), 309-329.
