Not only were there women who opposed suffrage, there still are. For instance, here's Central Missisippi Tea Party President Janis Lane in 2012:
I'm really going to set you back here. Probably the biggest turn we ever made was when the women got the right to vote. [...] Our country might have been better off if it was still just men voting. There is nothing worse than a bunch of mean, hateful women. They are diabolical in how than can skewer a person. I do not see that in men. The whole time I worked, I'd much rather have a male boss than a female boss. Double-minded, you never can trust them.
Source: The Jackson [Mississippi] Free Press
And here's self-described polemicist Ann Coulter last year:
Well, as you know, my position is that women should not have the right to vote. [...] No, we can still write books; we can run for office. [Interviewer: You just can't vote.] Exactly.
Source: Unfortunately this isn't easily available from a neutral source, but this article includes an actual audio recording of the interview