Funnily enough, works by RAW.

There is no prohibition of magical healing in construct traits, though some constructs are explicitly immune to magic except select few effects.

There is also no prohibition in the heal spell.

Technically, you can do it, but expect a heavy book thrown by your DM. He will also probably houserule it away, at least I personally would.

Note:

Can't remember anything on that in 3.5 either, though the description of Warforged contrasts the possibility of both special and positive-energy healing (emphasis mine):

As living constructs, warforged can be affected by spells that target living creatures as well as by those that target constructs. Damage dealt to a warforged can be healed by a cure light wounds spell or a repair light damage spell, for example, and a warforged is vulnerable to disable construct and harm. However, spells from the healing subschool and supernatural abilities that cure hit point damage or ability damage provide only half their normal effect to a warforged.

That leads one to the implication of impossibility of positive-energy based healing for a regular construct, even if it is not stated anywhere.

Spells that induce sleep

The following spells put one or more affected creatures to sleep.

• The 1st-level Sor/Wiz spell sleep [ench] (Player's Handbook 280) causes up to 4 Hit Dice of creatures to make Will saving throws. Failure means for 1 min./level the affected creature sleeps. The leading indirect cause of death among goblins, kobolds, and orcs for over 40 years. I know the question mentions it already, but it's here for completeness.
• The 3rd-level Sor/Wiz spell deep slumber [ench] (PH 217) is like the spell sleep except that it affects up to 10 Hit Dice of creatures.
• The 4th-level Sor/Wiz spell dragon breath [evoc] (Spell Compendium 73), if the brass dragon's breath weapon is picked, creates a 15-ft. cone of gas that has those within to make a Will save. Failure means the affected creature for 1d6 rounds sleeps.
• The 4th-level Sor/Wiz spell Melf's slumber arrows [ench] (Complete Mage 110–1) makes magical 1 or more arrows that—when they deal damage to a target that possesses up to 15 Hit Dice—cause that target also to make a Will saving throw. Success means that for 1 hour that creature's fatigued. Failure means that for 1 hour that creature sleeps.
• The 5th-level Sor/Wiz spell sleep mote [ench] (Sandstorm 121) creates a movable cloud that—when it stops in the space of a creature that's size category is Medium or littler—causes the creature makes a Will saving throw. Success means that the creature still takes some penalties. Failure means that the creature sleeps (duration of the sleep effect is unspecified, but the cloud's duration is 1 round/level).
• The 5th-level Sor/Wiz spell symbol of sleep [ench] (PH 291) weaponizes expensive graffiti so that the reader and nearby bystanders—none of whom can possess more than 10 Hit Dice—that fail a Will save sleep for 3d6×10 min.
• The 6th-level Dream domain spell dream sight [div] (Heroes of Horror 128), among other effects—obviously—, causes the caster to sleep. Probably not what you're looking for, but included for completeness.
• The 6th-level Sor/Wiz spell endless slumber [ench] (Complete Mage 103) causes one living creature within close range that fails its Will saving throw to enter a permanent sleep… except the creature may attempt a new saving throw once per day to end the effect. (A creature may opt not to make the saving throw because while in the sleep, the need for sustenance is abated. An interesting story-facilitating spell.)
• The 7th-level Sor/Wiz spell eye of the beholder [trans] (Book of Vile Darkness 94), among other effects, has a 10% chance of enabling the caster to use 1/round while the spell's duration continues an effect like the spell sleep except that the effect affects but one creature that possesses any number of Hit Dice.
• The 7th-level Sor/Wiz spell hiss of sleep [ench] (SpC 114–5) has 1 creature/level—each of which is within close range—make a Will saving throw. Failure means that for 1 round/level the creature sleeps.

The 0-level bard spell lullaby [ench] (PH 249) receives honorable mention for giving targets that fail their Will saving throws against its effect a −2 penalty on saving throws against sleep effects.

Also, the effect of the 3rd-level Sor/Wiz spell feign death [necro] (Tome and Blood 89) and the effect of the 6th-level bard spell rapture of the deep [ench] (Stormwrack 120) can be easily mistaken for sleep effects even though they aren't, technically, sleep effects.

Note: I suspect the question's goal is an attempt to determine the value of the Dragon #325 feat Potent Enchantment (77). (And, if not, maybe somebody searching for this is.) Player's Handbook spells affected by that feat’s benefit include animal trance, calm animals, hypnotism, and mass charm monster in addition to the aforementioned sleep and deep slumber. Other spells on this list are unaffected by the benefit of the feat Potent Enchantment, either because the affected creature's Hit Dice are fixed like in the symbol and arrow spells or because a creature's Hit Dice don't matter to the spell.