The 3560E is one of Cisco's more powerful stand-alone multilayer (i.e. it can also route) switches. For just phones, the port bandwidth demand should be low (i.e. 100 Kbps or less), and you may not need to route. So, a pure L2 switch with just 10/100 ports should work well and be much, much less expensive than a 3560E, although you might need POE ports.
On the issue of finding a device with 56(?) ports, you can interconnect switches to provide the port count you need, such as a 24 port switch connected to a 48 port switch. However, with something like phones, you should also consider ways to minimize single point of failure and perhaps have enough spare ports to repatch if you do lose a device.
Jon's recommendation of the 3750 is good, because you stack the devices so that you only have one logical switch to configure, and loss of one individual stack member doesn't stop the other units. (You can also mix different models within the stack.) Like the 3560, the 3750 is another multilayer switch. Both for that reason, and the stacking capability, it likely will be more expensive than independent L2 switches.
Assuming your L2 switches support a variant of STP, if you loop 4 24 port switches, loss of one will not stop the others from working and you'll still have 96 ports.
Within Cisco line up, the 2960 series should work well, see http://www.cisco.com/en/US/products/ps6406/index.html, but so might the Catalyst Express 520-24PC Switch, see http://www.cisco.com/en/US/prod/collateral/switches/ps5718/ps7238/product_data_sheet0900aecd8060aee4.html or Catalyst Express 500-24PC Switch, see http://www.cisco.com/en/US/prod/collateral/switches/ps5718/ps6545/product_data_sheet0900aecd80322aeb.html.
