You’ll want a long lens, ideally something that goes to at least 200mm. I use a 70-300mm lens for wildlife.

I would say look at Sony mirrorless like an A6000 and see if you can get an older used camera and lens for that budget. They had superior autofocus in the camera body years you’ll be able to get with that.

Hold a feather toy just above your lens to get them to look right at you.

Can you both be holding something, like could your partner be handing you a flower bouquet? For the book idea, what about sitting close to each other on a park bench reading the same book, or one of you holding a book and the other turning the page for them? Sitting at a picnic blanket and handing each other a sandwich?