It appears that some female birds do produce uneven sex ratios, and scientists are still working to understand how.
Here's one article that discusses a possible mechanism, and a quote from the article:
https://news.cornell.edu/stories/20...ther-birds-find-way-produce-more-progesterone
"Cornell University researchers think they understand the mechanism that several bird species use to bias the sex ratios of their offspring toward female.
"By experimenting with domestic chickens, they have determined that the presence of higher-than-normal levels of the hormone progesterone during the first meiosis -- the cell division that divides the sex chromosomes and genetically determines the sex of an offspring -- produces significantly more females. "
