Hi! I've checked with Conga and Salesforce, both have basically stated they cannot help with this issue. I have just now sent a case to DocuSign, but really hope for help soon if anyone knows.  

When the Opportunity Owner tries to click our (custom) button to kick off a Conga document that gets registered with DocuSign, she (and myself) get an error, "There was an issue processing the Composer Request" on clicking the "Continue" following document generation. The debug URL looks the same as the debug url on other Opportunities that have been registered successfully today. Checking with other support desks, here's what was suggested:

CONGA: This is a Salesforce error, the last time I saw this was due to Salesforce being unable to log a task against the record in question – this could be the case here, the document generates fine on the preview, but when the Docusign part of the process is invoked and they try to log a task in the related list it may be getting stuck there. I’d check that the Docusign related list permissions are all in place on the Opportunity object – and also I would check with Salesforce to see if they are having any issues on the APAC server pods as well (if that’s where this solution is running - myDomains means I can’t see the pod in the URL). I thought initially it may be the Salesforce issue with the field update in Conga but that runs through fine with the Docusign parameters removed. The error is on the Opportunity dataset in Debug URLs when clicking the custom button on this Opp then clicking Complete.

SALESFORCE: This is a custom url hack issue. Go to the development community and try for help.

So...here I am! 

https://composer.congamerge.com
?sessionId={!API.Session_ID}
&serverUrl={!API.Partner_Server_URL_290}
&id={!Opportunity.Id}
&templateid=a0S2000000LBA5r
&DefaultPDF=True
&DocuSignVisible=1

&DocuSignR1Id=00520000001agdk
&DocuSignR1Type=Carbon+Copy
&DocuSignR1Role=Carbon+Copy+1
&DocuSignR1RoutingOrder=1

&DocuSignR2Id=00520000003EYD4
&DocuSignR2Type=Carbon+Copy
&DocuSignR2Role=Carbon+Copy+2
&DocuSignR2RoutingOrder=1

&DocuSignR3Id=0032000001cXW3c
&DocuSignR3Type=Carbon+Copy
&DocuSignR3Role=Carbon+Copy+3
&DocuSignR3RoutingOrder=1

&DocuSignR4Id=0030J00001wHSUg
&DocuSignR4Type=Signer
&DocuSignR4Role=Signer+1
&DocuSignR4RoutingOrder=2
&DocuSignR4EmailSubject="Excel4apps Opportunity Registration Request"

&DocuSignR5Id=00520000000vOmZ
&DocuSignR5Type=Carbon+Copy
&DocuSignR5Role=Carbon+Copy+4
&DocuSignR5RoutingOrder=1

&DocuSignR6Id={!IF ($User.Id = '00520000001agdk', null, IF($User.Id = '00520000003EYD4', null, IF($User.Id = '00520000000vOmZ', null, $User.Id)))}
&DocuSignR6Type=Carbon+Copy
&DocuSignR6Role=Carbon+Copy+5
&DocuSignR6RoutingOrder=1

&DocuSignR8Id=00520000001agdk
&DocuSignR8Type=Carbon+Copy
&DocuSignR8Role=Carbon+Copy+7
&DocuSignR8RoutingOrder=3

&DocuSignR9Id=00520000003EYD4
&DocuSignR9Type=Carbon+Copy
&DocuSignR9Role=Carbon+Copy+8
&DocuSignR9RoutingOrder=3

&DocuSignR10Id=0032000001cXW3c
&DocuSignR10Type=Carbon+Copy
&DocuSignR10Role=Carbon+Copy+9
&DocuSignR10RoutingOrder=3

&DocuSignR12Id=00520000000vOmZ
&DocuSignR12Type=Carbon+Copy
&DocuSignR12Role=Carbon+Copy+10
&DocuSignR12RoutingOrder=3

&DocuSignR13Id={!IF ($User.Id = '00520000001agdk', null, IF($User.Id = '00520000003EYD4', null, IF($User.Id = '00520000000vOmZ', null, $User.Id)))}
&DocuSignR13Type=Carbon+Copy
&DocuSignR13Role=Carbon+Copy+11
&DocuSignR13RoutingOrder=3

&QueryId=[NoetixCont]a6h20000000HQMn?pv0={!Opportunity.Noetix_Primary_ContactId__c},[ShipToCont]a6h200000004CRz?pv1={!Opportunity.Ship_To_ContactId__c}
&TemplateGroup=Nothing

&UF0=1
&MFTS0=Sent__c
&MFTSValue0=true

&DS7Preview=1

&DS7=17

&DC={!IF (Opportunity.Valid_Noetix_Contact__c = false, "1", "0")}
&DCL=Process+stopped+.+ Document+already+sent+or+Noetix+Primary+or+Ship+To+contact+invalid+:+email+,+phone+and+title+are+required.