Being pregnant is a happy time but also a very precious time, whether it is a easy pregnancy or less easy, it should always be surrounded by postivity, as this has great influence on the wellbeing of the unborn baby. What can fathers do to enhance health and for his unborn baby development to get a better start in life, as children are so precious we want to get this right? Spiritual development of the unborn baby is also important and this is giving by the mother through Mitzvahs and good deeds. The unborn baby could benefit from Kosher food, but most importantly is a happy home, surrounding by postivity and a calm environment.
Pregnant women often sew a Sash during pregnancy, and when the baby is a boy the Sash can be used on the Torah for his Bar Mitzvah and an aliyah on Shabbos before his own wedding.
During pregnancy I do believe studying the Torah is important as the unborn baby could benefit from it, doing good deeds, having a Tzedaka box and performing Mitzvahs has a positive influence, and attending Shul more often, visiting the Mikveh more towards the end of the pregnacy and reciting Tehillim, the father can take it upon him to recite Tehillim 20 before going to bed. This is not what you must do, but it could be beneficial to the unborn baby and not in the least for yourself.
Ashkenazi Jews traditionally name their children after relatives who past away, to keep the memory alive of our loved ones. A baby boy receives after the Bris his name, as before the bris a baby boy has to not yet received his soul and that is the reason he cannot be named till after the bris.
When a girl is to be named, is just like with a boy, the father names his daughter, this happens as soon as possible after birth, preferable on the first Shabbos after birth and he is called up to the Torah, the naming ceremony is when the Torah is being read with a Minyan.
When the birth starts, we hang Shir Lamaalot in the room of the hospital or at home of the mother and the newborn, it is a safeguard for the mother during giving birth but also the fallowing days after the baby is born, for at least three days, this is to safeguard the mother when giving birth, which can been seen as dangerous, as still many things can go wrong and not to violate Shabbos laws, this can be found in Shulchan Aruch, Rambam and Shabbos 129a.
The father should not be in the room during the birth of his child.
Blessings after the birth of the baby by the father as he has to say thanks to HaShem, by reciting the blessing of HaTov VeHametiv for a boy. For a girl it is the Shehecheyanu, this blessing can only been done by seeing the baby girl.
Another custom is to hang after the birth the prayer of Tehillim 121 in the room of the mother and baby