My mother used to do this and as such I grew up with a house full of hand tinted B&W images...... when I experimented with this in photoshop I found the best and easiest technique is quite easy.
Assuming using Photoshop
create a saturation/hue adjustment layer and desaturate all colours down to the level you want for the colour/colours you want to leave in.
create a channel mixer adjustment layer, select "monochrome" check box and adjust the channel mix (you'll probably still want it predominantly red but mix in blue or green in (they affect the brightness so if you increase the blue or green you'll either need to pull down the red or use the master slider to decrease overall brightness).
using the layer mask on the channel mixer layer select a large soft brush at about 3% to 6 %, select black and paint a "hole" in the layer mask to allow colour to show through.... if you overdo it you change back to white for the brush and paint back over the area.
one thing I also do _sometimes_ is to duplicate the image layer, put it to "soft light" blending at about 25%-50% then run "displacement glow" filter with a high amount of noise on it to great the soft glow and add noise to an otherwise clean digital image.
In lightroom the process is even easier (assuming the colour you want to "hand tint effect" exists only in the area you want it to show up in the final image as Lightroom has no masking ability).
drop down to the HSL (Hue Saturation Luminosity) area of the develop window and pull down the saturation sliders to 0 (or there about) for all the colours you want removed and adjust the slider for the ones you want to keep up or down to get the level of saturation you want.
You can also use the luminosity to change luminosity of colour areas (even after they are desaturated) so to be able change to the emphasis/impact of certain areas.
these days I'm mostly using this technique to create extra emphasis in one are / deemphasise another area rather than creating hand tinted style images but the technique is much the same just now I usually leave things fairly saturated (or don't use the saturation/hue layer at all).
http://www.pbase.com/marxz/image/89015606/medium.jpg
http://www.pbase.com/marxz/image/93356576/medium.jpg
These two below have displacement glow applied:
http://www.pbase.com/marxz/image/86338078
http://www.pbase.com/marxz/image/90489211/medium.jpg