I find that if you dig deep enough there's usually a nugget of sense in even the craziest client requests. The words they use to express what they want are usually wrapped up in a hodge-podge of what they've seen and what they think is normal - but every profession has its own flavour of "a little knowledge is a dangerous thing". It could be worse, we could be doctors trying to tell patients that the drug they saw an ad for yesterday won't cure them, or mechanics trying to explain why the client's friend "who's really good with cars"
was wrong and it this really honestly isn't a simple fix.
I'm guessing in this case because I don't know the client, but I can imagine a few genuine, sensible desires which, when put through the meat grinder of limited knowledge and experience, could result in them asking for a marquee with a welcome message that 'pops'.
- They want movement that jolts a new customer into focus, actively pointing their attention to a start point and actively introducing chosen elements to the customer. If this is true, there are loads of things that use movement to focus on key elements which your client might like, if they are presented right. Outside of text transition effects, the obvious one is a carousel - a bit of a cliche maybe and often misused, but they can be very effective when done right. It's also probably the closest thing to a marquee.
- They instinctively know their customers like the personal touch and can feel intimidated by even the cleanest modern web design. They feel they want to reach out and hand-deliver a welcome message to their customers as a clear place to start and they want to push that message to the visitor like an enthusiastic host. If this is what they want, this Smashing article on website introductions might be a place to start getting ideas.
- They might know their audience like things at a slower pace and like things to come to them - more shopping channel than shopping arcade. So they like the idea of slowly, gently pushing things towards the viewer at a set steady pace. Maybe your client knows their demographic feels lost in the digital jungle, and a marquee is the closest thing your client can think of to throwing them a guiding rope. If this is what your client wants, you've got a really interesting design problem: you'll want to explore and re-imagine the varied world of website elements that work for a semi-passive audience. A few examples of the top of my head are using video and the kind of guided interfaces you sometimes see in interactive visualisations (Development Seed's homepage is a cool if slightly confusing example of this principle applied to web design in general - the general principle is, there's a clear smooth path, and you can diverge from it if you wish)
Never underestimate how well a good small business owner instinctively knows their audience, even/especially if they have no knowledge of design or of their lack of knowledge of design. (also never underestimate how ignorant of their audiences some middle managers in big companies can be...)
If you'll forgive a "when I were young" story.... I was a student on a consultancy team as part of a placement, working with a guy who ran a business selling traditional Scottish stuff. His website was a thing of nightmares: it played bagpipe music at full volume on page load. Everyone who'd worked with him had told him to remove the music, and he always refused and got defensive: the others thought of him as impossible to work with.
One day in casual conversation I found a way to casually ask about the bagpipe music in a friendly, interested way. It turns out he regularly got emails from bored, older diaspora Scots who loved listening to the music while shopping, and who said it made them feel at home. The guy was a natural salesman: he'd jump on this, enchanting them with the stories behind each piece of music, working in his other products, and before long these guys were loyal, regular customers, on first name terms. He was selling them high-value goods, and they were spreading the world about his merch.
After listening, I started making suggestions about how he could improve parts of the site he'd previously refused to budge on - suggesting prompts before playing the music, clearer music player controls, and general things like a site design and structure that encouraged personal communications. He was listening keenly and taking the suggestions on board, because he could see that I understood what he was really trying to do. Everyone else had been so struck by how obviously a bad idea it was to play non-consensual bagpipe music at people, they'd never stopped to figure out why this smart, successful guy thought it was a good idea.