You can use a tick (DateTime.Ticks for instance) but don't store the tick as simple string, encode the bits. If you use a long tick (64bit) you should consider ASCII85 encoding of the bytes so it wont exceed 10 symbols.
var tickBytes = BitConverter.GetBytes(DateTime.UtcNow.Ticks);
string encodedTicks = new Ascii85().Encode(tickBytes);
If you chose a 32bit tick, base 64 should be fine.
For a readable tick with precision to second (less precise than the previous solution)
long origin = new DateTime(2014, 7, 24).Ticks / TimeSpan.TicksPerSecond;
long customTicks = (DateTime.UtcNow.Ticks / TimeSpan.TicksPerSecond) - origin;
string readableTicks = customTicks.ToString(CultureInfo.InvariantCulture);
That will stay on 10 chars or less for ~300 years.