Yes, most hotel booking APIs let you send a special request along with the booking, but it helps to understand what that request can and cannot do.
When your customer books, there is usually a field where you can pass a short note to the hotel, such as a preference for a quiet room, a double bed instead of twin beds, a non smoking room, or a warning that the guest will arrive late in the evening. That note travels with the reservation and shows up on the hotel's arrivals list next to the guest name. Some suppliers accept free text, while others only accept a fixed set of options that you choose from, so what you are able to send depends on the supplier sitting behind the API rather than on your portal.
The honest part is that a special request is a request, not a promise. The hotel decides at check in whether it can be met, and that depends on what is free on the day. Nothing is confirmed in advance, so it is safer not to tell your customer that a room type, a floor or an arrival time is guaranteed. Requests that carry a cost, such as an extra bed, early check in or connecting rooms, are normally arranged and paid for at the hotel itself, so they sit outside what the booking covers.
If a request really matters to your customer, ask your supplier which requests they pass on and in what form, keep the note short and in plain English so nothing is lost, and contact the hotel directly closer to the arrival date to confirm.