Yes, you can send a special request with the booking in most cases, but you cannot promise your customer it will be honoured. A hotel booking API normally has a free text field, and often a short list of common requests such as a twin or double bed, a quiet room, a high floor, adjoining rooms or a late arrival. Whatever you type there travels with the reservation to the hotel, and it usually appears on the voucher as well.
The important part to explain to your customer is that a request is not a guarantee. The hotel decides at check in, based on what is free that night, and a busy property may simply not have a twin room left even though the request reached them. The one request that carries more weight is a late arrival, because it tells the front desk to hold the room rather than release it, so it is always worth adding when the guest lands after the evening.
What the field will accept varies by supplier. Some pass long free text through untouched, some cut it short, and some only accept requests chosen from their own list. A few will not read anything written in a language other than English, so it is safest to write requests in plain short English sentences and keep them to what really matters for that stay.
Before you rely on it, make a test booking with a request on it and check that the wording comes back unchanged on the confirmation you receive.