There is no mention of a literal suffix on the MSDN reference for Byte as well as in the C# 4.0 Language Specification. The only literal suffixes in C# are for integer and real numbers as follows:
u = uint
l = long
ul = ulong
f = float
m = decimal
d = double
If you want to use var, you can always cast the byte as in var y = (byte) 5
Although not really related, in C#7, a new binary prefix was introduced 0b, which states the number is in binary format. Still there is no suffix to make it a byte though, example:
var b = 0b1010_1011_1100_1101_1110_1111; //int