You could send your X,Y coordinates in "binary" or "ASCII decimal number strings". If you use a single 8-bit byte to send a value, yes you are limited to 0-255 ... but if your data object is two bytes, you get 0-65535, and so on.
Taking the binary approach may be a little advanced for you, so consider a second approach:
Assuming X=123 and Y=56, have Processing send "123,056\n" - to keep things simple, make sure each coordinate is 3 digits - to the serial port on which the Arduino is listening.
The Arduino code reads one character at a time starting with the X coordinate numbers 1-2-3, recognizes the comma as a command to start receiving the Y coordinate numbers, receives the Y-coordinate numbers 0-5-6, and recognizes the newline character to start looking for the next X value. This is called a simple "parser".
If you look at an ASCII character set you will see the numbers 0-9 grouped together, which makes it very convenient to convert ASCII numbers to binary ... just subtract the character '0' from each ASCII number character received. So '1' (which is decimal 31 in the ASCII table) minus '0' (which is decimal 30) = 1.
So back to the Arudino code loop. Receive the first character '1' which you know is the hundreds digit, subtract '0' to get 1, multiply this by 100, and save it in a variable = 100.
Now receive the next digit, the tens digit '2'. Do the '0' subtraction to convert to binary 2, multiply by 10 making it 20, add to the variable saved previously - now you have 120.
Now receive the last digit, the ones digit '3'. Do the '0' subtraction to get binary 3, no need to multiply, add to the variable saved previously - now you have 123.
Now receive the next character - it is comma - set a flag in your code to start receiving the Y coordinate. Process the characters 0-5-6 in the same manner as for X. When the newline character is received, the code reverts to receiving the next X coordinate.
There may be a function Integer.ParseInt() which does the same thing for you, but you will still need to detect the comma and newline and "split" the input characters into 3-character strings for the X and Y values.