Birds vs Rat vs Dogs

I'm not sure there is an answer to this, but I thought I'd ask. We have a bird feeder in our garden on which I hang a couple of seed feeders, another with peanuts in it, a suet block feeder and also a tray on which I sprinkle suet bits... it is these last that seems most popular. My dilemma is that we have a bold, frequently visiting rat which at first just took dropped seed from the floor, but now has started to climb the feeder and eat from the tray of suet bits. I don't really mind the rat, but my other half has stronger anti-rat feelings than I. Whilst I don't want to encourage the rat, I don't want to stop feeding the birds. To mix things up too, we can't put down any kind of rat poison because not only do I not agree with it but we also have two Dachshunds who have free run of the garden. Any thoughts on how I can keep all the visitors to my garden happy without encouraging the rat.