According to my calcs using the discharge equation Vout = Vin * e-t/Tau, assuming a 13V input and a minimum 2V output, the delay until discharge to 2V with a 1000 ufd capacitor and 39 Ohm coil is 0.073 seconds = 73 ms.
Matlab code:
Vin = 13; % assume a supply voltage
R = 39; % relay resistance in Ohms
C = 1000*10^-6; % timing capacitor in Farads
Tau = R*C; % time constant Tau
t = linspace(0,3*Tau); % graph from 0 to 3 Tau
Vout = Vin * (exp((-t/Tau))); % discharge equation
plot(t,Vout) % plot the discharge curve
ylabel("Voltage")
xlabel("Time - seconds")
grid on
[h,~]=legend("Discharge Voltage");
figure(gcf) % or shg command - pull plot to top
t = - (Tau * log(2/Vin));
fprintf("Time voltage will remain above 2V => %.3g seconds\n",t)
% include results from Command Window
% Time voltage will remain above 2V => 0.073 seconds
%
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Graph attached... You can see where the trace crosses 2V at a little over 70 ms. The MATLAB code will also run in Octave which is free.
I would use a capacitor rated at least 25V if not 50V.
The only equation you really care about is "t = - (Tau * log(2/Vin))". Calculate Tau as R (Ohms) * C (Farads), pick a dropout voltage (here it's 2V) and an input voltage Vin. Assuming you have accounted for all the parallel load on the capacitor, this equation should work fine.
In the world of Octave and MATLAB, log(x) returns the Natural Logarithm which is usually ln(x) on a calculator. The Common Logarithm (base 10) is log10(x).