A few ideas:
I would start by asking the tenants if they really care about the utility costs since Landlord is supplying the appliances. They may just agree to cover them, especially if Landlord offers to eat the appliance costs if they cover the utilities.
If that doesn't work and it is an issue for the tenants, I wouldn't do it. However, if you want to press on, here are a couple of ideas:
Install a coin-op washer and dryer and use the revenue to reimburse the tenants. Calculate costs with inline meters on the electric and water. You will need to read them and do some math, but this would allow you to calculate costs and evenly allocate them if they go 50/50. You can do this without a coin-op feature, but then you have to bill the tenants for small amounts which is just one more thing to have to track and follow-up on. You won't know who used more or less, so any complaints about volume are more issues. You can use a card reader on the coin-op feature to address that, but you are into micro-issues at that point that I wouldn't want to deal with.
A proposal: Tenants, installing separately metered water and electric lines that I pay for, then bill you for, will cost me $5,000 (or whatever). I would then pass that on to you in a rent increase of $100/month more/less. I'd rather not do that. Instead, can you just cover the utilities or go to the laundromat. This is just a heavier version of the first idea.