Persuade and convince in imperative, future and request form.

[dwni1]

For instance,
We organise a party and my friend needs me to convince my neighbour to come to that party.

Can my friend say
Imperative
1 Persuade your neighbour to come to the party.
2 Convince your neighbour to come to the party.

Request
3 Can you persuade your neighbour to come to the party?
4 Can you convince your neighbour to come to the party?

Can I say
I will persuade my neighbour to come to the party.
I will convince my neighbour to come to the party.
I am going to persuade my neighbour to come to the party.
I am going to convince my friend to come to the party.

Future

 

[teechar]

1 Persuade your neighbour to come to the party.
2 Convince your neighbour to come to the party.

You need something like "Try to" or "Do your best to" before either of those sentences to make them sound natural.

Request
3 Can you persuade your neighbour to come to the party?
4 Can you convince your neighbour to come to the party?

Those sound like questions about a person's ability. Again, add something like "Do you think you can" before the first verb.

Can I say
I will persuade my neighbour to come to the party.
I will convince my neighbour to come to the party.
I am going to persuade my neighbour to come to the party.
I am going to convince my friend to come to the party.

You can if you're absolutely sure of a successful outcome. Otherwise, add something like "do my best" or "try hard" after "will" or "going to".

 

[Rover_KE]

I don't like the use of 'convince' in this context.

See the Similar threads below.

 

[emsr2d2]

For instance,
We organise Let's say we're organising a party and my friend needs me to convince my neighbour to come to that party.

Can my friend say the following?
Imperative
1. Persuade your neighbour to come to the party.
2. Convince your neighbour to come to the party.

Request
3. Can you persuade your neighbour to come to the party?
4. Can you convince your neighbour to come to the party?

Can I say the following?
Future
5. I will persuade my neighbour to come to the party.
6. I will convince my neighbour to come to the party.
7. I am going to persuade my neighbour to come to the party.
8. I am going to convince my friend to come to the party.

Future

Please note my changes above.

All eight sentences are grammatically correct.
I agree with teechar that #1 and #2 would be improved by adding something at the start to make them sound less abrupt.
Although "Can you" should be used to ask about ability, a very large number of native speakers use "can" as a request.
I don't find "convince" as unnatural as Rover, mainly on the basis that you'll hear a lot of native speakers using it this way.