Code will associate a custom object to the contact associated to a deal.

associateCustomObjectToContact.js

// Import HubSpot Client Library and instantiate client with private app token
const hubspot = require('@hubspot/api-client');
const hubspotClient = new hubspot.Client({
    accessToken: process.env.HUBSPOTTOKEN // Access token associated with your private app (also be sure to include token in secrets)
});

// Helper function to get the associated Object ID of a specified Object Type
async function getAssociatedObjectId(objectType, objectId, toObjectType) {
    let obj = await hubspotClient.crm.objects.associationsApi.getAll(objectType, objectId, toObjectType);
    return obj.results[0].id;
}

// Helper function to associate a custom object to a contact
async function associateCustomObjectToContact(objectTypeId, customObjectId, contactId) {
    const AssociationSpec = [{
        "associationCategory": "USER_DEFINED",
        "associationTypeId": 33 // To get this value you need to make a GET request to https://api.hubapi.com/crm/v3/schemas/{objectTypeId}
    }];
    hubspotClient.apiRequest({
        method: 'PUT',
        path: `/crm/v4/objects/${objectTypeId}/${customObjectId}/associations/contact/${contactId}`,
        body: AssociationSpec
    })
}

exports.main = async (event) => {

    // Define variables
    const objectTypeId = '2-116144011'; // Custom Object "objectTypeId" (this will be different for you)
    const objectId = event.object.objectId // Currently enrolled Custom Object Record Id

    // Get associated Deal ID
    const dealId = await getAssociatedObjectId(objectTypeId, objectId, 'deal');
    console.log('DEAL ID: ' + dealId);

    // Get associated Deal Contact ID
    const contactId = await getAssociatedObjectId('deal', dealId, 'contact');
    console.log('Contact ID: ' + contactId);

    // Associate Object to Contact
    try {
        const apiResponse = await associateCustomObjectToContact(objectTypeId, objectId, contactId);
        console.log('SUCCESS: ' + JSON.stringify(apiResponse, null, 2));
    } catch (e) {
        e.message === 'HTTP request failed' ?
            console.error('ERROR: ' + JSON.stringify(e.response, null, 2)) : console.error('ERROR: ' + e)
    }
}

HI @jackcoldrick90 the contact property is a single line text property.
On the partner object, it's a numeric field.

But if need be, I can still adjust the property type (I only have 8 (test) contacts with a value for this currently)