Collagen Hydrolysates are available for sale:
Alfa Vitamins Collegen Hydrolysate Nutrition Supplement, 120 Count

This makes it a very promising supplement but the cost of the dosage ratios recommended would be insane but could be up to 25% additional height.  There are 120 pills for $10.  A 50lb kid would take 25 a day to meet the dosage requirements.  So that would be about $2.50 a day.  Which I guess is not that bad.

Porcine Skin Gelatin Hydrolysate Promotes Longitudinal Bone Growth in Adolescent Rats.

"Collagen hydrolysates (CHs) are mixtures of peptides obtained by partial hydrolysis of gelatin that are receiving scientific attention as potential oral supplements for the restoration of osteoarticular tissues. The aim of this study was to evaluate the effectiveness of CHs for promoting longitudinal bone growth in growing rats. An in vitro study was carried out in osteoblast-like MG63 cells and the most effective CH on bone formation was selected among 36 various CHs. An in vivo study confirmed the functional effects of a selected CH with molecular weight of <3 kDa on longitudinal bone growth. CHs dose-dependently promoted the longitudinal bone growth and height of the growth plate in adolescent male rats, whereas gelatin failed to affect longitudinal bone growth. Insulin-like growth factor-1 and bone morphogenetic protein-2 in the CH treated group were highly expressed in the growth plate."

"Collagen is the major constituent of the connective tissues in vertebrates, comprising 30% of total body protein. The denatured form of collagen is referred to as gelatin and is commonly used in foods, pharmaceuticals, cosmetics, and others. To increase the solubility of gelatin, partially hydrolyzed gelatin products have been prepared and are referred to as collagen hydrolysates (CHs)."

3-Week old male Sprague-Dawley rats were used.

"Longitudinal bone growth in normal adolescent male rats was 404.0±11.6 μm/day, and administration of 50 and 250 mg/kg gelatin failed to promote the longitudinal bone growth. However, treatment with 250 mg/kg of CH significantly increased the longitudinal bone growth exhibiting 468.4±27.4 μm/day."<-The dosage for the alfa vitamins collagen above is 1000mg.  So maybe a human should actually take a larger dosage.  250mg/kg is actually pretty insane dosage in terms of cost but growth was over 25% more. That's 550mg/lb.  So a 200lbs individual would have to take 100 pills a day.  50mg/kg still increased height just not statistically significantly.

Here's the growth plate under Collagen Hydrolysate(growth plate height was increased by 11%).

"CHs with molecular weights <3000 Da that is able to increase IGF-1 and BMP-2 protein expression in growth plate, and consequently promote longitudinal bone growth in growing rats."<-the molecular weight of the supplement above is not listed.  Looking it up Collagen Hydrolysate has an average molecular weight of 2000-5000 Da so it's possible that the molecular weight here is over the threshold but humans may be able to tolerate the higher moleculate rate than rats.

Food consumption doesn't seem to be measured but gelatin could serve as sort of a control to that.