For an engagement session on a rainy day, here are some ideas that you can suggest to the couple to capture some beautiful and romantic moments:
Find an indoor location with natural light - Look for a cozy café, a library, or an art gallery with beautiful lighting. This can create a romantic and intimate atmosphere and also protect the couple from the rain.
Use an umbrella - Take advantage of the rain and use an umbrella as a prop to create some romantic shots. Have the couple stand close together under the umbrella and experiment with different poses and angles.
Use reflections - Use the reflections on the wet pavement or in puddles to create unique and creative shots. Ask the couple to stand or sit near the reflection to create an interesting composition.
Get wet - If the couple is willing, take some photos of them walking in the rain and holding hands. This can create a fun and adventurous atmosphere and also capture the couple's natural chemistry.
Use a window - If you are shooting indoors, use a window as a frame for the couple. Have them stand close together and capture their reflection in the window or use the raindrops on the window to add some interest to the shot.
Use props - Use rain boots, raincoats, or an umbrella as props to add some fun and personality to the shoot. This can also create a cohesive theme for the photos.
Nighttime rain photography - If the couple is comfortable with it, take advantage of the city lights reflecting off the rain to create some stunning nighttime photos. Experiment with long exposures and light trails to create a romantic atmosphere.
Remember to communicate beforehand and discuss preferences and ideas for the shoot.