Using CTA data,

Type of Diesel Fuel Energy Content (BTU/gallon LHV) Natural Gas Properties Energy Content (LHV)
U.S. conventional diesel  128,450 Energy - Volume Basis   983 BTU/CF
Low-sulfur diesel  129,488 Energy - Mass Basis 20,267 BTU/lb

However, Wikipedia's Gasoline Gallon Equivalent article uses 129,500 BTU/gallon LHV as the basis for their GGE calculations, which is reasonably close to the CTA's Low-Sulfur diesel value.  The US DoE recommended data in the Transport Energy Data book as the basis.  However, in the USA, the Department of Commerce in each state determines the basis for pricing so there is no national standard for energy content.  Presumably, the natural gas utilities will also incorporate their own pipeline gas analysis in the DGE calculation as well.  The Wikipedia's GGE article also uses 900 BTU/CF for natural which is close to the rule of thumb value of 1000 BTU/CF HHV.

Using Low-sulfur diesel,  129,488 BTU/gallon / 983 BTU/CF = 131.73 CF/gallon .  Therefore, 1 DGE = 131.73 CF of natural gas.

Similarly, 129,488 BTU/gallon / 20267 BTU/lb = 6.389 lb/gallon.  Therefore, 1 DGE = 6.389 lb of natural gas.

1 gallon = 129,488 BTU
1 BTU = 1/129,488 gal
1 MMBTU = 1/129,488 x 106 gal  = 7.72 gal

1 litre = 3.785 gal, therefore 1 DLE = 6.389/3.785 = 1.688 lb

1 DLE = 1.688 lb x 2.204 lb/kg = 3.721 kg

Often, CNG is advertised in terms of GGE.  So 129,488 BTU/gallon / 113,602 BTU/gallon = 1.1398 or  ~1.14 GGE = 1 DGE

Similarly, a Diesel Litre Equivalent (DLE) relative to a Gasoline Litre Equivalent (GLE) is also 1.398 GLE = 1 DLE

In Terms of Diesel:

Price Posted Multiply by To Get Diesel Equivalent Price
$/kg 0.003721 ¢/DLE
$/lb 6.389 $/DGE
$/GGE 1.1398 $/DGE
$/GLE 1.1398 $/DLE