@Grant Griffiths
Prepare a nice presentation for your clients highlighting their strengths e.g income, jobs, letter of recommendations etc. while disclosing the reasons for their low scores. Personal letters may help.
Higher deposits and prepaid rents could help sweeten the pot, but first impressions help. As a private landlord, I get bombarded with leads whenever I have vacancy. When someone contacts me with a lot of information, it makes my job easier and I am more open to having a conversation with them.
Drive around the neighborhood and look for signs for rent and for sale. These owners are more likely "old school" and don't have an online presence.
Another idea is to discuss with your client if they can pay you for your services vs charging the landlord commissions. Some private landlords don't want to deal with realtors as they have to pay. I am not an agent so I don't know if this is against any regulations. I always pay an agent his/her fees if they bring me more qualified renters than what I can find myself.
Good luck!