The success of autonomic computing has led to its popular use in many application domains, leading to scenarios where multiple autonomic managers (AMs) coexist, but without adequate support for interoperability. This is evident, for example, in the increasing number of large datacentres with multiple managers which are independently designed. The increase in scale and size coupled with heterogeneity of services and platforms means that more AMs could be integrated to manage the arising complexity. This has led to the need for interoperability between AMs. Interoperability deals with how to manage multi-manager scenarios, to govern complex coexistence of managers and to arbitrate when conflicts arise. This paper presents an architecture-based stigmergic interoperability solution. The solution presented in this paper is based on the Trustworthy Autonomic Architecture (TAArch) and uses stigmergy (the means of indirect communication via the operating environment) to achieve indirect coordination among coexisting agents. Usually, in stigmergy-based coordination, agents may be aware of the existence of other agents. In the approach presented here in, agents (autonomic managers) do not need to be aware of the existence of others. Their design assumes that they are operating in 'isolation' and they simply respond to changes in the environment. Experimental results with a datacentre multi-manager scenario are used to analyse the proposed approach.