Generally speaking, tourism carrying capacity has four dimensions: environmental, economical, social and psychological. It might be necessary to focus on one of these dimensions if your current project is a small one.
The methodology will depend also on the context of your study. For example, is the purpose to determine the number of visitors that a specific site can handle sustainably, in which case you'd need to look at visitor numbers, quality of visits, and visitor management methods; or is it to set limits on development of tourism facilities, such as the maximum number of hotels and hotel rooms on an island along with associated transport and other infrastructure, which would require assessment on wider impacts on island systems, planning frameworks and planning controls?
There are various planning methodologies available for such studies, including strategic environmental and social impact assessment methodologies, visitor surveys, etc. Also, in the island / coastal context, it is important to look at tourism within a framework of integrated coastal zone management.
Specifically focusing on tourism, there are several planning methods and approaches that are available including the Recreational Opportunity Spectrum (ROS) and Limits of Acceptable Change (LAC) methodologies. You may find the following could be useful starting points:
Managing Tourism & Biodiversity - it includes a number of checklists at the end, as well as a section on planning methodologies, including ROS and LAC - http://www.cbd.int/doc/programmes/tourism/tourism-manual-en.pdf
Water and Land Recreation Opportunity Spectrum - www.usbr.gov/recreation/publications/WALROS_Handbook_2011.pdf
Limits of acceptable change - Fact sheet - Department of Sustainability, Environment, Water, Population and Communities, 2012
I believe the choice of a method would depend on response you are looking for and available financial resources. If you are short in resources, I think the Cifuentes (1992) methodology is appropriate as it provides a good overview of the environmental and social and psychological carrying capacity. Unfortunately, it does not incorporate the economic carrying capacity. Please check below:
Hope it helps!
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I prefer longitudinal studies that involve the host community to look at setting limits or thresholds of acceptable change and sustainable tourism development. Also, it doesn't hurt espouse quality over quantity when designing products and marketing activities.
There is no standard method for tourism carrying capacity. The closest that one might find is in relation to methods used for Environmental Impact Assessments, which incorporates all of related dimensions e.g. environment, economy and social.