Kei is correct.
To add further detail. Combat happens in steps I'm sure you know this.
1. (Precombat) use instants/effects usually to remove attackers or resolve triggers that happen at the start of the attack Step.
2. (Assign attackers) The active player chooses attacking creatures and taps them unless something says otherwise (IE: vigilance), this does not use the stack and cannot be responded too in anyway. These creatures are now considered attacking and any triggers that say "when this creature attacks do x" will trigger and go on the stack. A round of priority is passed if there are any such triggers.
3. (post Attacking Step), after attackers are declared before blockers are declared, there is a round of priority to play spells and effects. Here for instance you could play a creature with flash and use it to block in the next step.
4. (Assign blockers) The defending player, chooses which creatures they use to block which attackers, assuming there are not blocking restrictions IE: unblockable, flying etc. This does not use the stack and you cannot play effects. here the attacker also decides damage order. Which creatures will receive damage first then 2nd etc. Any triggers that happen "when this creature blocks" go on the stack and resolve with a round of priority.
5. (Post blocking Step). After blockers are declared, there is a round of priority. Instants and other activated abilities can be played here. Here you an return a blocker to your hand to prevent damage to it, or buff a blocker with a giant growth for a favorable trade.
6.(First strike damage Step/ Damage Step). _First, if there is a first strike or double strike creature, a new and separate damage Step is created with all the following rules, then the 2nd "regular" damage step happens with the same rules. Only creatures with first or double strike deal damage in the first strike damage step._ If there is more than one blocker, or if there is trample, damage is assigned here, and the points of damage are allocated to the blocking creatures and/or players. Tramplers must assign lethal damage to blockers before any remaining damage can be assigned to players. No instants or abilities can be played in this step and damage all resolves at the same time. State based effects (IE: creatures with lethal damage) must be resolved here and any triggers that happen when creatures go to the graveyard go on the stack and a round of priority resolves.)
7. (Post combat cleanup). There is a round of priority here, all creatures are still considered attacking and blocking at this step and effects that target attackers and blockers can still be played here.
that's generally correct, i think. I may have slipped up on a minor detail.
Some hypothetical notes about your example.
Lets say for example, your trampling sliver had first strike, then as stated above you would deal damage first, before the creatures without first strike. So, 2 damage to the flyer, then 3 to the player and they don't get a chance to deal damage back since they're in the grave yard due to state based actions.
lets say, for whatever reason the cockatrice had first strike, then it deals it's deathtouch damage first, before any "normal" damage can be dealt by the trampler and the defending player takes no damage.
Now, what if the trampling sliver had Double strike? It gets to deal damage twice, first strike and normal damage. It would deal 2 to the flyer, killing it then 3 to the player ,then 5 again to the player. UNLESS!!! it didn't have trample. Then the damage stops there. only trample can make damage carry over to the player. So without trample, even double strike damage stops with the blocker.
Furthermore, if the trampling sliver had deathtouch it could deal only 1 point of damage to the blocker then 4 to the player, (death touch makes even 1 point of damage lethal, and the rules specify that you must deal _lethal_ damage to a blocker before trample can carry over to the player.
Also just to be thou rough, Blockers can't deal combat damage to attacking players even if they have any of the abilities mentioned.
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