My Grandpa brought a putter to the delivery room when I was born. It's an old Bullseye with a 37" shaft (still too long for me, and likely always will be) but he didn't actually push the game on me. He would just take me with him when he'd go out to practice for half an hour and give me a putter and a ball, then set me loose upon the greens. He'd occasionally bring a small wedge with him and let me use that as well, just telling me to pretend I was putting the ball with it.
Beyond that, he would give me a certificate entitling me to a local junior golf program for my birthdays. The instructor was (and still is) very beginner friendly and gives simple advice to younger kids such as always teeing up the ball or making smaller swings. He also made it fun by setting up range baskets out about 15' away and giving you a quarter for each time you knocked one over.
My grandpa kept it fun for me with games. He'd put a leaf on the green with a quarter underneath it and tell me I could keep the quarter if I got my putt to stop on top of the leaf from a distance away (5' at first, then got further). We'd have competitions to see who could chip it the closest from around the green, and he'd get me an ice cream cone afterwords if I managed to get it closer than him.
When we played he had me start by teeing off at the 100 yard marker. The rules were that after 6 shots you would just pick it up and set it on the green. You then had 4 putts to try and get it in the hole. Once I started getting it on the green consistently in 2 or 3 shots, he moved me back to the 150 marker, then the 200 after that. We played a fairly small 9 hole course with plenty of shade, which meant that once I got past the 200 yard marker I would play from the red tees.
I remember my biggest goal, once I moved back to the red tees, was to beat my grandpa. The first time I did it, I remember telling everyone who was in the clubhouse when we got back in since I was still only 7 or 8 (shot a 54 to his 55). All the while I would take the occasional lesson from the same instructor who did the junior golf program. The biggest part of that was that, while I learned the basic fundamentals, the pro wouldn't give me too much to think about at any one time. He'd give me something like "try gripping it this way" or "try changing this one thing" at the end of a lesson to practice with until the next lesson I'd take a couple months later.
I used 3 different sets of golf clubs before I bought my current regular set. Two AMF kids sets (probably $100-200 each) that he had a friend cut down at first, then add plugs in later. Lastly, he got me a somewhat nicer set before my current clubs with a Callaway junior golf set ($300ish) that lasted me from 7-12. That was when I was first introduced to a "driver" with 17* of loft. Every set before had only up to a "3-wood" of 24* to help me hit the ball in the air easier. This was a big help and confidence booster for me.
He never pushed me to play golf, but would ask if I wanted to come with whenever he would play. I'd always jump at the chance to be with my grandpa, especially since he would take us in his old 280z convertible in the summer. Most of all, he just made the game a lot of fun for me to play.
The summer after my 8th grade year was when he took me out to look at my current irons (Eye 2's). He had told me that I could play for the high school team if I wanted, possibly earning a scholarship, and that he would help me with a new set of clubs if I would try my best. We got the Eye 2's and put in GS95 shafts since they were lightweight ($150 total there). We went to a nearby Golfsmith and managed to get a deal trading my old clubs in, getting a G10 3-wood and Driver for $200 with ProLaunch Red shafts in them (I think the current model was G20's or something, so they were on sale). Finally, on a trip to Michigan that summer, we saw G10 18*, 21*, and 24* hybrids on sale used for $30 each. I paid him back by doing weedeating, lawnmowing etc. around his home for the summer. After saving up I managed to get myself some Ping Tour-S wedges that I liked the look of, and still just used my old putter.
After all that, I was given a local public golf course junior membership for my birthday from my parents, which allowed me to play at a discounted rate, and I went to practice often. I would still make games out of it, and made friends with the head pro's son. I got a lot of free golf and range balls hanging out with him, not to mention cheesy fries at the clubhouse! I soon started taking lessons from a different pro than before, who really helped me start to understand the golf swing more than I did before. After playing in summer tournaments and two years of high school golf, I ended up where I'm at. I still love to play and will try to go out as often as I can. I got a job at the golf course through the pro I take lessons from and can golf or hit range balls for free at all of the city courses because of it.
Anyways, long story short, just try to keep it fun and make it all about different games. Just keep in mind that a quarter, ice cream cone, or candy bar can turn an otherwise boring drill into a fun competition when practicing and always phrase it so that you're asking if he wants to come play with you on the golf course. Doing that should at least get you a lifelong golf partner, which I know was my Grandpa's original intention.