It sounds like you all would be better off without a fax machine altogether, honestly. If you sign up with an online fax service, like eFax or MyFax, you won't need to worry about not having a second phone line since incoming faxes would just go to your email or online fax account.
Plus there are a bunch of online fax companies that have pay-per-fax options, like SFax's Freedom Plan - it's $24 a year and works on a credit system. Once you go through 100 faxes, you can buy more credits as needed.
In case you're interested, here's a site I've used before (it's actually where I got all my info): http://findafax.com/