Well I'm confused about this too. I thought you couldn't, but the Pay & File Guide (for tax year 2007 so I'm assuming applies to 2008) suggests you can, for fixed, lift and weight charges, even from private contractors:
"Service Charges [525]
All service charges paid in full and on time in the previous calendar year (2007) to:
i) Local Authorities for:
domestic water supply,
domestic refuse collection, or disposal
domestic sewage disposal,
ii) group water schemes for domestic water supply,
iii) independent contractors for domestic refuse collection or disposal,
qualify for tax relief at the standard rate of tax (20%) in 2007.
The Finance Act 2006 introduced new limits on the amount of relief that can be claimed. The limits from the 1st of January 2007 are as follows:
The total tax relief that can be claimed for both fixed charge payments made (including lift charges and
pay by weight) and bin tags purchased in 2006 will be subject to an overall limit of €400
The relevant amount paid in full and on time in the previous calendar year should be entered.