How to Permanently solve MySQL error 2002 (HY000)

I hope everyone is well. I have a problem on my cloud server with 2GB of RAM and 40GB Hard Disk that's hosting a Wordpress website that receives around 1000-2000 hits a day. My problem is that MySQL is always crashing and my only option is to reboot the server. I noticed that logs were not enabled so I enabled them and here is what i found:

150207 17:31:42 [Note] Plugin 'FEDERATED' is disabled.
150207 17:31:42 InnoDB: The InnoDB memory heap is disabled
150207 17:31:42 InnoDB: Mutexes and rw_locks use GCC atomic builtins
150207 17:31:42 InnoDB: Compressed tables use zlib 1.2.3.4
150207 17:31:42 InnoDB: Initializing buffer pool, size = 1.2G
InnoDB: mmap(1285636096 bytes) failed; errno 12
150207 17:31:42 InnoDB: Completed initialization of buffer pool
150207 17:31:42 InnoDB: Fatal error: cannot allocate memory for the buffer pool
150207 17:31:42 [ERROR] Plugin 'InnoDB' init function returned error.
150207 17:31:42 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed.
150207 17:31:42 [ERROR] Unknown/unsupported storage engine: InnoDB
150207 17:31:42 [ERROR] Aborting
150207 17:31:42 [Note] /usr/sbin/mysqld: Shutdown complete

I am guessing this has something to do with memory allocation or some settings in my my.cnf file. These are the contents:

[client]
port                           = 3306
socket                         = /var/run/mysqld/mysqld.sock

[mysqld_safe]
socket                         = /var/run/mysqld/mysqld.sock
log_error                      = /var/log/mysql/mysql_error.log

[mysqld]
user                           = mysql
pid-file                       = /var/run/mysqld/mysql.pid
socket                         = /var/run/mysqld/mysqld.sock
port                           = 3306
datadir                        = /var/lib/mysql
thread_cache_size              = 4
table_open_cache               = 800
table_cache                    = 800
key_buffer                     = 32M
query_cache_type               = 1
query_cache_size               = 64M
query_cache_limit              = 8M
innodb_buffer_pool_size        = 1G
innodb_io_capacity             = 2000
innodb_read_io_threads         = 64
innodb_thread_concurrency      = 0
innodb_write_io_threads        = 64
log_error                      = /var/log/mysql/mysql_error.log
slow_query_log                 = 1
slow_query_log_file            = /var/lib/mysql/ib_slow_log.log

Any help will be greatly appreciated.

Regards!