Even if you were allowed to "fog" the site it would have to be done repeatedly and often if you expected to keep the mosquitoes down to a very low level. Since your mosquito problems are not nearly as seasonal as they are in more temperate climates your problem would be around all year long. The ideal approach would be to prevent the adult mosquitoes in the first place, which means attacking the problem at its source - those sites where there is standing water that the larvae are developing in. Many of these sites could well be right on the property of the hotel, and these you can go after in some manner. A careful inspection of the property may reveal many aquatic sources, such as tree holes that can be filled or drilled to drain them, low areas with standing water that can be filled or drained, planters and other artificial containers that retain water that can be drained, removed, drilled, etc. Rain gutters are notorious for clogging with debris and filling with water, and these need to be inspected and maintained. Nearby dump areas may have containers, old tires, etc., etc., and an inspection of these kinds of areas would be useful. 

Wherever you find standing water in the form of ponds, slow-flowing streams, lakes, etc. you may be able to treat using a larvicide, such as one of the bacteria formulations (Teknar, BTI Briquets) or the IGR (Altosid). These products are considered to be quite environmentally friendly as they are specific to the arthropod larvae in the water, primarily mosquitoes that live in the water zone where the active ingredients will be. Some of them can provide 30 days or more of control of mosquito larvae, killing them before they become the biting adults. Different formulations are available depending on the size of that aquatic environment. Treating the larval habitats is going to be your best way to prevent the adult mosquitoes at this hotel site if you are able to do so. 

Another option may be barrier treatments using residual insecticides, but this also depends on whether or not the management allows you to "spray" around the area with guests nearby. Barrier treatments rely on applying the residual contact insecticide to the resting sites of the adult mosquitoes, killing them as they spend time on that surface. This may be in trees or shrubbery or under the eaves of roof lines, within out buildings, under decks, etc. This can be a very effective supplement to the larval control, but it will only last for a few weeks at best, and would need to be redone as well. 

So, I suggest you discuss these options with the customer, and make the point that if they expect a 100% reduction in the adult mosquitoes it is not realistic. Nothing is going to accomplish that. What you can do is to greatly reduce the numbers of adult mosquitoes and at least reduce the problems and complaints.