There are two aspects to this problem:
a) generating the sine values.
b) creating an analog output.

The generation problem is pretty easy. You can do a lookup table in an FPGA; that lookup table is what's implemented in that ROM you can't find, and the smallest FPGAs have more resources anyway. You need a counter at some nominal sample frequency to read the lookup table.

Or you could use a microcontroller to generate sine values, again using a lookup table or perhaps just calling a math library with a sine function. Use a timer to get a new value on a regular interval.

The second half of the problem is generating the output. Most micros have built-in DACs, so you simply scale the sine function output (a real number between -1 and 1) to the DAC's output range. Or just configure the lookup table to give you exact DAC outputs.

Or connect an SPI or I2C or I2S DAC to your micro or FPGA output.

You could even do PWM to generate the sine wave analog output.

Lots of options!

-a