I wonder if the Altera DE1 and DE2 have the same UART? I got access to both the DE1 and the DE2 and I see a similar question but the manual isn't specific which FPGA is applicable.
When talking about FPGAs we need to distiguish between "hard cores" and "soft cores".
A "hard" core is a section of the chip dedicated to a particular function. Your design just tells the synthisis tool how to hook it up.
A "soft" core is a core implemented in FPGA logic, it may be supplied by the FPGA vendor, it may be bought from a third party, it may be freely downloaded from somewhere like opencores, it may be written by yourself. Some "soft" cores may be written in generic verilog, others may be specific to a device familily.
I have never seen a FPGA with a hard UART. SO you are going to have to use some kind of soft implementation.
The DE1 and DE2 use the same FPGA family so it shuld be possible to use the same UART cores on both of them.
The problem I have found with alteras cores is they assume you are using altera's avalon bus system. I have found it's often easier to write serial transmit/receive code from scrath than to figure out how to glue the rest of my design to an inappropriate bus system.