The formula for the volume of fluid in a horizontal and level cylindrical tank with flat ends
V = l * (pi*r^2/2 - r^2*arcsin(1-h/r) - (r-h)*sqrt(h(2r-h)))
where V is volume,
l is the interior horizontal length of the tank cylinder
r is the interior tank radius,
h is the height of fluid in the tank as measured from the bottom of the horizontal cylindrical tank interior and must be less than 2*r.
(If the tank isn't level then all bets are off)
Once you have the formula any method that accurately gives you the height of the fluid will suffice, including a yardstick.
Since right now the customer is already measuring the fluid and entering it in a log manually and it seems that the issue is with using the look up table then the cheapest and simplest solution is a spreadsheet with the above formula built in. Customer enters the fluid height, and it spits out the result. The spreadsheet becomes the usage log. You could use a formula in excel using excels built in functions, or you could also program a custom function in Excel VBA, eg tankvolume(l,r,h) and that way deliver software and a billable service (or I'll do it for you for a small fee
).
If you want to automate the measuring then there are already some good suggestions. Magnetostrictive sensors will probably give you the best resolution for clean inert fluids. If the tank is actually elliptical or not level then load cells are an excellent way to measure the tank contents.
You will have the least amount of resolution in your measurement when the tank is half full, or in your tank, at 32 inches. At that level you need a resolution of .025 inches to resolve 1 gallon. .025 inches is easy for a magnetostrictive sensor. Its also easy for a 100" WC pressure sensor mounted at the bottom of the tank.
IFM efector makes a submersible one you can insert from the top of the the tank and just let it lay on the bottom of the tank. Even a 12 bit A/D will give you the needed resolution with one of those, although I would recommend 14 bit or better. If the fluid has a specific gravity different from water its a simple multiplication to scale a 100" WC sensor to compensate.