In search of a physical covenant, some families wrap the baby in a tallit, a four-corned ritual garment. Sometimes the tallit was used as a huppah at the parents' wedding. Other times it is a gift to the baby to use when she is able.
Some words to use with this ritual:
As we prepare to enter you into the covenant, we take this tallit, the tallit with which we began our family, our huppah, and embrace you in it. As we wrap you in our tallit, we enter you into the family of our people and covenant you to God, our Torah, and the people Israel.
בָּרוּךְ אַתָּה אֲדֹנָי אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם אֲשֶׁר קִדְּשָׁנוּּ בְּמִצְוֹתָיו וְצִוָּנוּ לְהַכְנִסָה בִּבְרִתַם שֶׁל אַבְרָהָם וְשָׂרָה
Masculine: Barukh atah adonai eloheinu melekh ha'olam asher kid'shanu b'mitzvotav v'tzivanu l'hakhnisah biv'ritam shel Avraham v'Sarah.
בְּרוּכָה אַתְּ יָהּ רוּחַ הָעוֹלָם אֲשֶׁר קִדְשָׁתְנוּ בְּמִצְוֹתָה וְצִוַּתְנוּ לְהַכְנִסָה בִּבְרִתַם שֶׁל אַבְרָהָם וְשָׂרָה
Feminine: B'rukhah at ya eloheinu ruah ha'olam asher kid'shatnu b'mitzvoteha v'tzivatnu l'hakhnisah bi'vritam shel Avraham v'Sarah.
Blessed are You, Adonai our God, Sovereign of the Universe, who has commanded us to enter this child into the covenant of Abraham and Sarah (or the People Israel).