During the time of Trajan in Roman Britain, AD 97-103, this is what an invitation to a birthday party looked like. From Vindolanda, a fort along the frontier where Hadrian built his wall.
British Museum Collection, image used under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
Claudia Severa writing her sister, Lepidina:
"Claudia Severa to her Lepidina, greetings. On 11 September, sister, for the day of the celebration of my birthday, I give you a warm invitation to make sure that you come to us, to make the day more enjoyable for me by your arrival, if you are present. Give my greetings to your Cerialis. My Aelius and my little son send him their greetings. I shall expect you sister. Farewell, sister my dearest soul, as I hope to prosper, and hail."
More on Roman Birthday celebrations in this Forbes article from 2016. For a coin of this period, here is a denarius of Trajan struck AD 107-108.
Trajan, AD 98-117, AR Denarius, Rome mint, struck mid AD 107-108
Obv: IMP TRAIANO ΛVG GER DΛC P M TR P, laureate bust right, slight drapery on left shoulder
Rev: COS V P P S P Q R OPTIMO PRINC, trophy on tree stump with one round shield, two hexagonal shields; at base, two javelins, two shields, and a sword
Ref: RIC II 147