Answer: The Shulchan Aruch (OC 307:1) writes that one shouldn’t make plans on Shabbos for what they are going to do after Shabbos. The Mishna Berura (307:1) explains that this prohibition only applies to actions that are otherwise forbidden on Shabbos.
As there is a machlokes as to whether one can discuss mitzva matters that involve melachos, he writes that it is best to avoid such conversation. However, there would be no issue in talking about such a mitzva if it means that they are more likely to perform it afterwards. Thus, one is allowed to pledge money to tzedaka when receiving an aliya, etc.
R’ Chaim Falagi (Lev Chaim 3:72) writes that as one gets such simcha, enjoyment, from inviting people to special occasions, one may do so on Shabbos. R’ Ephraim Greenblatt (Rivevos Ephraim 8:185:1; 8:500) quotes this but adds that one shouldn’t hand out printed invitations, however, to avoid paying the postage.
R’ Ovadia Yosef (Yalkut Yosef, Shabbos 307:21) however, disagrees. While it is certainly ideal to distribute such invitations during the week, one may distribute invitations to a seudas mitzva on Shabbos when necessary. One must be careful not to give one to anyone who may come to carry it home outside of an eruv, however.
In conclusion, one should try one’s utmost not to distribute such invitations on Shabbos. Ideally, one should bring them to shul before Shabbos and tell friends about them for them to take home afterwards.