Is there any good working MODBUS TCP master library available for Arduino?
Check out the library Modbus-TCP on Github. It has the facility for all the function codes as asked. It has provision for Wiznet W5100 and ENC28J60 Ethernet IC. All tested with Arduino Mega. See the well documented example code for the Wiznet module in the library.

For detailed knowledge about the library, read the index.html inside the doc folder of the library.

Here is an example code explaining a few function codes for the Arduino Mega and a W5100 module. 

/*
  This is Modbus test code to demonstrate all the Modbus functions with 
  with Ethernet IC WIZNET W5100 

  ModbusTCP is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.

  ModbusTCP is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with ModbusTCP.  If not, see &lt;http://www.gnu.org/licenses/&gt;.

  Adopted from ModbusMaster for RTU over RS-485 by Doc Walker
  Modified by Narendra Dehury for TCP.
  copyright @ phoenixrobotix.com

*/
#define WIZNET_W5100 1

unsigned int param_value_int[7];
#include &lt;Ethernet.h&gt;

IPAddress ModbusDeviceIP(10, 10, 108, 211);  // Put IP Address of PLC here
IPAddress moduleIPAddress(10, 10, 108, 23);  // Assign Anything other than the PLC IP Address

byte mac[] = { 0xDE, 0xAD, 0xBE, 0xEF, 0xFE, 0xE1 };


#include &lt;ModbusTCP.h&gt;

ModbusTCP node(1);                            // Unit Identifier.

void setup()
{

  pinMode(4, OUTPUT);
  digitalWrite(4, HIGH);                      // To disable slave select for SD card; depricated.

  Serial.begin(9600);
  delay(1000);
  Ethernet.begin(mac, moduleIPAddress);
  node.setServerIPAddress(ModbusDeviceIP);
  delay(6000);                                // To provide sufficient time to initialize.

}


void loop()
{
  uint8_t result;

  node.setTransactionID(random(100));           // Not necessary; but good to distinguish each frame individually.
  result = node.readHoldingRegisters(1, 12);    // Read Holding Registers

  Serial.println(result, HEX);
  if(result != 0)
  {
    Serial.println("TimeOut");

    delay(6000);
  }

  int len = node.getResponseBufferLength();           
  Serial.println("Response Length: " + String(len));// See the length of data packet received.
  for (byte j = 0; j &lt; len; j++)
  {
    Serial.print(node.getResponseBuffer(j));       // Inspect the data.
    Serial.print(" ");
  }
  Serial.println();
  node.clearResponseBuffer();
  delay(100);




  node.writeSingleRegister(5, 3);                  // Write single register
  Serial.println(result, HEX);
  delay(500);



  for (byte i = 0; i &lt; 5; i++)
  {
    node.setTransmitBuffer(i, (i+100));
  }
  node.writeMultipleRegisters(2, 5);               // Write multiple register
  Serial.println(result, HEX);
  delay(500);



  node.writeSingleCoil(20, 1);                     // Write Single coil
  delay(500);



  node.setTransmitBuffer(0, 0b1010101001010101);

  node.writeMultipleCoils(20, 16);                 // Write multiple coils
  delay(500);
  result = node.readCoils(20, 18);
  len = node.getResponseBufferLength();
  Serial.println("Response Length: " + String(len));
  Serial.println(node.getResponseBuffer(0), BIN);


  node.clearResponseBuffer();
  delay(5000);
}