What ingredients can be used to make fried rice slightly sweet?

Often there's no secret sauce that restaurants use, but plain old bog-standard sugar. I know it's boring, but there you go. They also may be using bottled sweet and sour sauce, which is also boring, but readily available in many supermarkets.

All is not lost, however, as if you want some more authentic ingredients then there are plenty of options. In my kitchen (which isn't big enough to satisfy my capacity requirements for exotic ingredients otherwise this list would be bigger) I have several ingredients which impart sweetness to Asian dishes:

• Palm sugar: more of a Thai than a Chinese ingredient, but I use it for many different cuisines. It imparts a slightly syrupy flavor. In the UK this can be found in any big grocery store in the Asian section.
• Sweet soy syrup: Also can be found under the name Kecap Manis, this is an Indonesian ingredient. It is basically teriyaki concentrate, it's salty, very sweet, and has some spices in it. I use it in all sorts of Asian cooking (and I sometimes add it to gravy to darken and sweeten it), and it would be my choice for the dish you want to make. I would add it instead of soy sauce until I have the sweetness I'm looking for, then add regular soy to bring the saltiness to the right level. Adding a little bit of water helps loosen it up
• Honey: not a purely Asian ingredient of course, but honey can be magic anyway. The floral notes may be just what you need

Now for the sour:

• Tamarind: you mentioned tamarind in your post as something to sweeten, but tamarind is actually quite sour. I use paste at home, it lasts forever in the fridge
• Lime or lemon juice: of the two I prefer lime juice when making Asian cooking sour. I can't quite say why.
• Rice vinegar: This is a very commonly used souring agent, I use it most often in Chinese cooking, and it would be my choice for a fried rice dish

Also worth mentioning is Mirin - a reduced-alcohol Sake, usually with a bit of salt added. It's used widely in Japanese cuisine. I personally don't use it much, but it's worth having in the flavor arsenal.

I would suspect they're using Shari, or "sushi rice". This is prepared with sugar (your sweet) and rice vinegar (your sour), and can easily be made at home. This beginner recipe on Just Hungry suggests the following ratio:

For the amount of rice we cooked in the first part (360cc, or 2 rice-cooker cups, or 1 3/4 U.S. cups) we will need:

3 tablespoons rice vinegar (45cc) (1 1/2 tablespoons per cup)

1 tablespoon fine sugar (1/2 tablespoon per cup) (I used sucanat; white granulated or superfine sugar is fine)

up to 1 teaspoon finely ground salt (1/2 teaspoon or less per cup) (I used sea salt)

This is added to the rice immediately after cooking; you pour it over the top, then sort of chop-and-fold with the rice paddle to distribute evenly. To avoid damage to rice-cooker bowls, Maki also suggests doing the mixing in a metal bowl (to help the rice cool faster).

When the rice is cooked, seasoned, and cooled, it can be fried with whatever ingredients you like.

Thicker soy sauces typically have molasses or other sugar added, which would result in a much sweeter result. (some are thickened with starches, though).

If you're making an Indonesean style fried rice (Nasi Goreng), you'd use Ketjap Manis instead of typical soy sauce, which is almost a cross between molasses and soy sauce (with ginger and other spices, as GdD mentioned)

For those times before I had a source of Ketjap Manis, I'd fold in a few shredded carrots to add extra sweetness ... and I still typically do, as I just like mine pretty vegetable-heavy.