Hi, Please change your code to :

trigger setRenewalOwnerContact on Opportunity (before insert) 
    {
     for ( Opportunity opty : Trigger.new ) 
        {
            if (opty.Opportunity_Contact__c == null) 
                    {
                    for(Contact con : [SELECT id FROM Contact WHERE Accountid = :opty.Accountid AND Contact_Type__c = 'Renewal Owner' LIMIT 1] ) 
                                 {
                                    opty.Opportunity_Contact__c = con.id;
                                 }
                    }
        }

 For test, Create a test contact with type = 'Renewal Owner' and create a test opportunity. Insert the opportunity.

You might want to first re-write your trigger so that you don't have a SOQL query inside the for-loop.  Otherwise, you'll probably hit a governor limit if you every insert a bulk of Opportunities.

Try it this way.

trigger setRenewalOwnerContact on Opportunity ( before insert ) {

   Map<Id,Id> acctToContactMap = new Map<Id,Id>();

   Set<Id> acctIds                         = new Set<Id>();

    for( Opportunity o : Trigger.New ) {

          acctIds.add( o.AccountId );

    }

    for( Contact c : [ select AccountId, Id from Contact where AccountId IN :acctIds and Contact_Type__c = 'Renewal Owner'  ] ) {

           acctToContactMap.put( c.AccountId, c.Id );

     } 

    for( Opportunity opty : Trigger.New ) {

          if( opty.Opportunity_Contact__c == null && opty.AccountId != null ) {

              opty.Opportunity_Contact__c = acctToContactMap.get( opty.AccountId );

          }

    }

}

To test it.

public class OpportunityTriggerTest {

            static testmethod void testOne() { 

                       Account a = new Account( Name = 'Test Account' );

                       insert a;

                       Contact c = new Contact( FirstName = 'Testy', LastName = 'Testerson', Contact_Type__c = 'Renewal Owner', AccountId = a.Id );

                       insert c;

                       Opportunity o = new Opportunity( Name = 'Test Opp', StageName = 'Prospecting', CloseDate = System.Today(), AccountId = a.Id );

                       insert o;

                       o = [ select Opportunity_Contact__c from Opportunity where Id = :o.Id ];

                       System.assertEquals( c.Id, o.Opportunity_Contact__c );

            }

}