I am afraid I had to be reminded of this by an Anonymous contributor who made a comment on this site... but I am revising this post now. The gender of your child may be determined by an even/odd date, either by the date of your marriage or the date on which you give birth.
As I stated previously, I have not tested this myself in my own games, so will NOT add it to any of my guides. I would appreciate any feedback from players on this topic.
(Note on 27 August: Thanks to all who posted their data here! It appears that the gender IS random, after all, but I would be happy to receive more data if players wish to continue to post it here.)
Anonymous stated that, if you propose on an even day, causing your wedding to fall on an odd day, your child will be a boy. If you propose on an odd day, causing your wedding to fall on an even day, your child will be a girl. This was based on the premise that your wedding would follow 7 days after your proposal, which is not necessarily the case. If a Festival day intervenes, the Wedding will be set a day later... if there are two Festival days or intervening Rival Marriages, then two days later, and so on.
I had been given information to the effect that a child born on an even day would be a girl and that a child born on an odd day would be a boy. As I had not been able to test this in my own games, it did not go into my guide, but a number of players had emailed me to ask why they could not have a girl in Cute, which caused me to publish a post here based on the Anonymous comment.
I since decided that the information is too conflicted to be posted as definitive. What I am publishing instead is a request to players to post their own game results here. What was the date of your proposal? What was the date of your wedding? When was your child born in Cute and was it a boy or a girl?
Ryva posted a comment to the effect that she knew some one who had a boy on an even day. I welcome comments from other players giving their results. I would prefer results from your own game rather than 'I knew some one who had...' because I know from my own experience that one sometimes forgets the precise date of an event in Harvest Moon. If you have a current game, however, your child's birthday as well as your Anniversary Date will be on your Calendar. Please post here! Thank you.