Deploy Test Suite?

No, it does not look like they are available via Change Set as they are just data records in the ApexTestSuite and TestSuiteMembership tables. You will probably need to script the creation of the test suites in the target org in the same way that you would create data in Custom Settings, etc.

From the Force.com IDE Release Notes - Spring '16 Update:

To create or customize a test suite, use the Developer Console or the API. See Salesforce Help: Manage Sets of Apex Test Classes with Test Suites or

Object Reference for Salesforce and Force.com: ApexTestSuite, TestSuiteMembership.

Update:

Upon further reading, it looks like you can query them via SOQL but you must insert the records via an API call as DML is not allowed here. Sounds like they behave similarly to Custom Metadata records.

Insert a TestSuiteMembership object using an API call to associate an Apex class with an ApexTestSuite object. (ApexTestSuite and TestSuiteMembership aren’t editable through Apex DML.)

To remove the class from the test suite, delete the TestSuiteMembership object. If you delete an Apex test class or test suite, all TestSuiteMembership objects that contain that class or suite are deleted.

SFDC provided SOQL Query:

SELECT Id FROM TestSuiteMembership 
          WHERE ApexClassId = '01pD0000000Fhy9IAC'
          AND ApexTestSuiteId = '05FD00000004CDBMA2'

ApexTestSuite is now a formal type of metadata that can be retrieved and deployed from an org. See https://developer.salesforce.com/docs/atlas.en-us.api_meta.meta/api_meta/meta_apextestsuite.htm