Is there a avalon master interrupt receiver template?

In order for the DMA to work with the UART you would have to enable Avalon-MM flow control. This is a depreciated feature so I would just stay away from it. Normally people will hook up the UART to Nios II so that it can service the interrupts. The UART that ships with SOPC Builder doesn't buffer data so using a DMA might be overkill for what you are attempting to do.

I think the Nios II driver for the UART always checks that there is valid data in the rx holding register or that there is room for more data in the tx holding register. A simple DMA is not capable of these control based decisions. You could make a statemachine with a master connected to it to do this for you if you are not using Nios II in your system.

I recommend listing out what you are attempting to do so that we can give you more ideas.