Is there a reason why you want to cover it? Because that becomes a safety hazard that most venues will not accommodate. Guests are well aware and understand that permanent venue fixtures (flooring, walls/paint, ceiling, etc) are out of your control and they don’t expect you to have bottomless pockets to alter the venue aesthetics. Once guests walk in, they will register the existing decor for less than a fraction of a second and then focus on other guests in attendance who are waiting for you to arrive.
You may be able to rent a dance floor from a local party rental business which costs money but they won’t provide carpeting or tiles for the entire room. When you say they are offering a stage, that is elevated right? So which part specifically are you wanting to cover that you feel guests will be judgmental about? Do you have venue photos for reference?
I would highly recommend talking to the venue and determining what their legal fire safety codes are at minimum before renting or purchasing flooring. Having coordinated and set up for commercial events myself, the building and fire/health safety codes can be really difficult to work with but are of upmost importance to maintain. The venue will know exactly what is and isn’t allowed. That’ll give you a good idea of what you can do and how much floor you can cover
Your venue should have stage skirting. I'd go neutral black first to not draw attention to the stage height, then add a floral arrangement or Mr. and Mrs. sign on the floor in front of your sweetheart table. I don't think you need anything on the stage itself. But if you like, you can use an outdoor rug (durable, thinner) under your sweetheart table. I'd just focus on what you can see, rather than what you can't. Good luck.