I happen to be in this exact situation right now. Software: www.ptengine.com. It's a web analytics and heatmap SaaS that is actually pretty good. Really useful for CRO work. The analytics are more precise than GA for sites with tons of traffic, the heatmaps are the best I've seen (blow CrazyEgg out of the water), you can segment/filter way better than with competitor software, and it's free for sites that get less than 25k views/mo. Up till now they've done some sponsored posts (written by the blog owners), PPC (ended up being too pricey per user acquired), and SEO (rankings are 5th page for heatmap-type terms, not enough time IMO to get organic results). I suspect a CPA+ of $3-5 per user would be attractive to affiliates, but I'm game to hear your experience in previous campaigns you've run and advice.
Top 2 tactics: Existing Users and Industry Influencers.
First, leverage the existing user base. Incent referrals with $5 for every new free user they get to sign up and start using PT Engine for a new domain.
Second, reach influencers and offer them the same deal when they tweet / post to / email their audiences.
Make the offer a 60 day free trial instead of the standard 30 day so that they are providing value to the people they refer as well. This is critical - don't make them feel sleazy, make them feel (and look) like heroes to the connections they share PT Engine with.
That's $9k to get 1800 users, leaving you $1k for graphics, referral tracking system, administrative costs. I assume the $10k budget does not include your time - if it does you'll have to reduce the incentive, which will definitely make it less appealing.
If you want to dive deep on reaching influencers, schedule a call with me at www.clarity.fm/ryandraving