You can do this fairly easily with Apps script or a macro. If you know the starting cell (that contains the formula) and destination cell (where you want the formula pasted) will always be the same,
The script is very easy. For example, if copying the formula from cell C2 to cell D3, see below. Once pasted, the formula will (should) update itself.
function pasteFormula() {
var spreadsheet = SpreadsheetApp.getActive(); //gets the current 'active' sheet (wherever the mouse is)
spreadsheet.getRange('C2').copyTo(spreadsheet.getRange('D3'), SpreadsheetApp.CopyPasteType.PASTE_FORMULA, false); //pretty self-explanatory. The 'false' on the end is an indicator regarding transpose (change rows to cols, or cols to rows)
};