* Police say suspect al Shabaab supporters
* Nine-year-old boy killed in church grenade attack
* Violence follows Kenyan attack on militants in Somalia (Recasts, changes dateline)
By Abdisalan Ahmed
GARISSA, Kenya Sept 30 (Reuters) - Two police officers were shot dead in Kenya on Sunday in the northern town of Garissa close to the border with Somalia, police said, hours after a child was killed in a grenade attack on a church in Nairobi.
Kenya has been hit by a series of grenade and gun attacks since it sent troops into Somalia last October in pursuit of Islamist al Shabaab militants whom it blamed for kidnapping its security personnel and Western tourists.
The killing of the police officers and the attack on the church came days after Kenyan troops launched a surprise offensive on the southern Somali port of Kismayu, al Shabaab's last stronghold, forcing the rebels to flee.
Most of the inhabitants of Garissa, where the police officers were shot, are ethnic Somalis and the town is located only 180 km (111 miles) from Kenya's border with Somalia.
Herman Ndiema, Garissa's deputy police chief, told Reuters the two officers were killed as they walked to a technical college they had been assigned to guard. Their killers drove up to them in a taxi, shot them dead, and then jumped out to steal their guns, he said.
"We suspect sympathisers of the al Shabaab militant group were behind the attack and we have sealed all exit routes to nab them," Ndiema said.
The stolen guns, G3 rifles, were later recovered a short distance from the scene of the attack, a regional administrator said. Security was stepped up in the town with members of the security forces patrolling it by car.
Earlier in the day, a nine-year-old boy was killed and three other children wounded when a hand grenade was thrown into a Sunday school session in a church in the capital Nairobi, police and medical staff said.
Police said attackers threw the grenade into the Sunday school service in St. Polycarp's church on Nairobi's Juja Road.
The grenade exploded, spraying the children with shrapnel and fatally injuring the boy.
"We suspect this blast might have been carried out by sympathisers of al Shabaab," said Charles Owino, a police spokesman.
"These are the kicks of a dying horse since, of late, Kenyan police have arrested several suspects in connection with grenades," he said.
Police had warned there was a heightened risk of attacks soon after the Kenya Defence Force led an assault against the rebels in Kismayu under cover of darkness on Thursday, local newspapers said on Sunday.
They said police had found bomb making equipment in a bag on a bus carrying passengers from Garissa to Nairobi on Friday. All 60 passengers on board had been detained after no one admitted ownership of the bag, the papers said.
Masked assailants launched simultaneous gun and grenade raids on two churches in Garissa in July, killing at least 17 people. (Additional reporting and writing by Duncan Miriri in Nairobi; Editing by Andrew Osborn)