Forecasting future currency exposures I have a data set (about 60 observations for each variable) for monthly operating income for a Japanese company denoted in EUR, USD, and JPY, and their respective currencies. I believe there is linear relationship between the currencies and the respective operating income denoted in the currencies. However, the first differences in operating income and currencies are random.

What is the best way to forecast the exposure of the future short-term month's operating income?

I have translated the foreign income to JPY and added them together with their domestic operating income, and then use moving average, weighted moving average and trend line to forecast the next month (into the future).

I have also used the first differences/increments of the operating incomes and their respective currencies to make them stationary, and to find the regression and coefficient. However, I don't know how to use the results to forecast.

Are there any other models that produce better outcomes for this fairly limited sample set?
I believe that you may be looking at a spurious relationship. You are looking at the same data transformed by a scaling factor (the currency) and regressing it on itself. Of course they will be related. If they weren't scaled, they would be perfectly co-linear. 

What you really want to know is if there is an effect of changes in the relative value of Yen to USD or Euros on the operating income of the company. 

You should start by visualizing this relationship by graphing it. Graph the relative value of Yen in your time series, then graph operating income in your time series. Do they move together? Look for structural breaks. For instance, they may have only begun to move together in the last year, that can really mess up an econometric model if you don't account for it.

After you have finished analyzing it graphically, I suggest reading up on co-integration and the Engle-Granger method. Some literature that are good places to start are: Stock and Watson(1988), and Engle and Granger(1987). 

This part of time series econometrics enables you to work with variables that are NOT STATIONARY. One problem with first-differencing such as you mentioned in your question, is that it throws away the very relationship you want to know about. The Engle Granger method enables you to analyze the relationships that matter economically, and is still statistically sound.

The world of time-series economics is a lot of fun, but make sure you stay grounded in the economics behind your data. Don't ignore the little things in your data, they may be the most meaningful. Don't be surprised if the relationship you thought was important actually is not important. That tells you just as much as if it is!

There's so much to talk about with the fascinating area you are delving into but I hope this can be of interest to you.