If you have money to spend you can use ground penetrating radar or other remote sensing method.
But if you want cheaper solution, you can use inverse hydraulics modeling (e.g. by using EPANET/WaterGem) but you need to have flowrate and presure data for several points of measurement. You can also use analytic approach (calculate pipe diameter based on pressure and flow variabales (e.g. simplfied bernoulli or Darcy Weisbach equation).
Another approach is by looking for flowmeter installed. You can find the diamater of the flowmeter or if you know the permanent/average flowrate, you can determine diameter based on flowmeter specs. An example is for 40 m3/h flowrate, the diameter of flowmeter would be around 50-65mm and the pipe would be most likely around 50-65mm as well.
GPR cant give diameter , it is only for depth , you have providing me theoretical process which is not possible , Watergems also required pipelie diameter for modelling.
The technology of passing an intelligent or callipar pig through the pipeline will reveal many other aspects as well like Corrosion, Erosion, Ovality, Thinning, profile of change in diameter across, location of changes etc. The agencies who are specialized in this will help you.
This technique is extensively used in Oil & Gas sector for Crude Oil & Product pipelines. There is need for pig launching & receiving faclity. In oil & Gas sector its a permanent feature. In your case it can temporarily done by the party engaged for the purpose.
You could try ground penetrating radar for an outside diameter or inserting a measurement pig for inside diameter. The pig will be able to give you various types of condition assessment (cracks, wall thickness etc) as well.
If you want a good estimate, slowly turn a gate valve and count the number of turns between fully open and fully closed. Pipe diameter in inches (sorry about that) is roughly (turns - 3) /3
Or, ask someone who operates the pipeline. Valves should be turned twice annually or they will not work when you need them.
Be aware of water hammer. Return valve to normal position.